Influence of process conditions on the auto-ignition ... - Lirias

KATHOLIEKE UNIVERSITEIT LEUVEN FACULTEIT INGENIEURSWETENSCHAPPEN DEPARTEMENT WERKTUIGKUNDE AFDELING TOEGEPASTE MECHANICA EN ENERGIECONVERSIE

Celestijnenlaan 300A, B-3001 Heverlee (Leuven), België

INFLUENCE OF PROCESS CONDITIONS ON THE AUTO-IGNITION TEMPERATURE OF GAS MIXTURES

Promotor: Em. prof. dr. ir. J. Berghmans Copromotor: Prof. dr. ir. F. Verplaetsen

Proefschrift voorgedragen tot het behalen van het doctoraat in de ingenieurswetenschappen door Frederik NORMAN

Juni 2008

KATHOLIEKE UNIVERSITEIT LEUVEN FACULTEIT INGENIEURSWETENSCHAPPEN DEPARTEMENT WERKTUIGKUNDE AFDELING TOEGEPASTE MECHANICA EN ENERGIECONVERSIE

Celestijnenlaan 300A, B-3001 Leuven, België

INFLUENCE OF PROCESS CONDITIONS ON THE AUTO-IGNITION TEMPERATURE OF GAS MIXTURES

Jury: Prof. dr. ir. E. Aernoudt, voorzitter Em. prof. dr. ir. J. Berghmans, promotor Prof. dr. ir. F. Verplaetsen, copromotor Prof. dr. ir. E. Van den Bulck Prof. ir. J. Peeters Prof. dr. ir. J. Degrève Prof. dr. ir. B. Merci (Universiteit Gent)

UDC 614.8

Juni 2008

Proefschrift voorgedragen tot het behalen van het doctoraat in de Ingenieurswetenschappen door Frederik NORMAN

© Katholieke Universiteit Leuven - Faculteit Ingenieurswetenschappen Arenbergkasteel, B-3001 Leuven, België Alle rechten voorbehouden. Niets uit deze uitgave mag worden verveelvoudigd en/of openbaar gemaakt worden door middel van druk, fotokopie, microfilm, elektronische of op welke andere wijze ook zonder voorafgaandelijke schriftelijke toestemming van de uitgever. All rights reserved. No part of this publication may be reproduced in any form by print, photoprint, microfilm, or any other means without written permission from the publisher. Wettelijk Depot: D/2008/7515/69 ISBN 978-90-5682-960-5

To Ilse and Janne

Voorwoord

v

Voorwoord Een zelfontsteking wordt bepaald door het evenwicht tussen de warmteproductie ten gevolge van de chemische reacties en het warmteverlies naar de omgeving. Daardoor kan een zelfontsteking heel traag op gang komen en pas na lange tijd tot ontsteking komen. Dankzij de hulp van vele personen kende mijn doctoraat geen dergelijk verloop. Aan het einde van mijn doctoraatsonderzoek wil ik daarom nog eens iedereen bedanken die in kleine of in grote mate heeft bijgedragen tot de realisatie van deze doctoraatsthesis. In de eerste plaats wil ik mijn promotor, prof. Jan Berghmans, en mijn copromotor, prof. Filip Verplaetsen, bedanken voor de kansen, het vertrouwen en de vrijheid die ze mij gegeven hebben om dit explosieonderzoek uit te voeren. Zonder jullie jarenlange inzet voor het explosieonderzoek was het niet mogelijk geweest dergelijke hoogstaande experimenten uit te voeren. Jullie hebben mij binnengeloodst in de boeiende wereld van de explosieveiligheid. Ook de andere leden van de examencommissie, prof. Erik Van den Bulck, prof. Jozef Peeters, prof. Jan Degrève en prof. Bart Merci wil ik bedanken voor de interesse en het kritisch nalezen van mijn doctoraatstekst. Prof. Etienne Aernoudt bedank ik voor het opnemen van de taak van voorzitter. Ik dank het Instituut voor de Aanmoediging van Innovatie door Wetenschap en Technologie in Vlaanderen (IWT-Vlaanderen) dat door middel van een specialisatiebeurs mij de afgelopen 4 jaar financieel gesteund heeft. Uiteraard was mijn doctoraatsonderzoek niet hetzelfde geweest zonder de aanwezigheid van mijn collega’s. In de eerste plaats wil ik Luc en Filip van de explosiegroep bedanken. Luc, samen met jou heb ik mijn eerste explosieproeven in de bunkers uitgevoerd en meteen werd duidelijk welk gevaar dergelijke proeven inhouden. Jouw werk rond zelfontsteking was voor mij van onschatbare waarde en vormde de basis van mijn doctoraat. Filip, bij jou kon ik steeds terecht met mijn explosievragen. Eveneens bedank ik je voor het toffe gezelschap tijdens de talrijke conferenties. Voor mijn experimentele opstelling kon ik steeds beroep doen op de kennis en ervaring van de techniekers. Hans, Ivo en Jos, merci voor jullie hulp en de vele babbels. Verder wil ik ook mijn bureaugenoten (Wim, Frederik en Frederic) bedanken om mijn bureautijd een pak aangenamer te maken. Tenslotte wil ik alle andere (ex-)collega’s bedanken, van wie ik de namen niet zal opnoemen opdat ik niemand zou vergeten, voor de babbels, de TME-weekends, de koffiepauzes, ... Dankjewel. Omdat het werk niet het enige is wat belangrijk is, wil ik eveneens mijn familie en vrienden bedanken. Een groot woord van dank gaat naar mijn ouders die me altijd hebben gesteund en bij wie ik steeds terecht kon. Merci moeke en papa. Als laatste, maar zeker niet minst belangrijk, wil ik mijn twee vrouwen bedanken. Ilse, jij staat steeds aan mijn zijde. Tegen jou kan ik alles kwijt. Jij bent mijn luisterend oor, je bent mijn ruggensteun, kortom je bent mijn grote liefde. Twee en een half jaar geleden zijn we in het huwelijksbootje gestapt. Dit leek een grote stap, maar deze dag verdwijnt in het niets in vergelijking met de geboorte van onze dochter, Janne. Janne, je bent nu nog heel klein,

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maar toch reeds een groot wonder. Janne, jij geeft zin aan ons leven. Je vult ons leven met vele verrassingen. Ilse en Janne, aan jullie draag ik dit werk op.

Heverlee juni 2008

Frederik Norman

Voorwoord

vii

Abstract Many chemical processes use combustible gases and vapours at elevated pressures and high temperatures. In order to evaluate the auto-ignition hazard involved and to ensure the safe and optimal operation of these processes, it is important to know the lowest possible temperature at which spontaneous ignition of these gases and vapours takes place. The auto-ignition temperatures (AIT’s) found in literature usually are determined by applying standardised test methods in small vessels and at atmospheric pressure. However, since the AIT is not constant but decreases with increasing pressures and increasing volumes, these AIT values are often not applicable in industrial environments. The lack of auto-ignition data at elevated pressures and the lack of comprehensive auto-ignition models are the motivations for this study. Therefore the present study consists of an experimental and a theoretical simulation part. The experimental study consists of the determination of the auto-ignition limits of methane, propane and butane mixtures at elevated pressures up to 3 MPa for a wide range of concentrations. It is shown that the auto-ignition limits decrease significantly with increasing pressure. The concentrations that are most sensitive to auto-ignition are high concentrations and depend on the initial pressure. The auto-ignition limits of the propane/butane mixtures correspond well with the auto-ignition limits of the component with the lowest auto-ignition temperature, which is n-butane. The location of the auto-ignition areas could explain the observations of the upper flammability limits at elevated temperatures and pressures of propane and n-butane mixtures. The numerical study focuses on the modelling of the auto-ignition process of methane/air mixtures at elevated pressures. First a zero-dimensional approach is adopted, based upon the model of Semenov. The chemistry is modelled by means of a detailed reaction mechanism. A methane reaction mechanism of the British Gas Corporation shows the best agreement with the experimental results. To take thermal and mass diffusion and the natural convection inside the vessel into account, a two-dimensional model is built including the kinetic mechanism. A CFD-model is used to compute the heat transfer and the buoyant flows inside the vessel. The coupling of the reaction mechanism to this model results in an accurate prediction of the auto-ignition conditions at elevated pressures. This model is also used to investigate the volume dependency of the auto-ignition temperature for both spherical and cylindrical vessels.

viii

Abstract

Korte samenvatting Vele chemische processen maken gebruik van brandbare gassen en dampen bij verhoogde drukken en temperaturen. Om het zelfontstekingsrisico te kunnen inschatten en om de veilige en optimale werking van deze processen te verzekeren, is het belangrijk om de laagst mogelijke temperatuur te kennen waarbij spontane ontsteking kan optreden. De zelfontstekingstemperaturen (AIT’s) die in de literatuur beschikbaar zijn, zijn meestal bepaald volgens gestandaardiseerde methodes in kleine volumes en bij atmosferische druk. Aangezien de zelfontstekingstemperatuur niet constant is maar daalt bij toenemende drukken en toenemende volumes zijn deze AIT’s niet rechtstreeks toepasbaar voor industriële condities. Het gebrek aan zelfontstekingsdata bij verhoogde drukken en grote volumes en het gebrek aan uitgebreide modellen van de zelfontsteking waren de drijfveren van deze studie. Daarom bestaat deze studie uit een experimenteel en een numeriek gedeelte. De experimentele studie bestaat uit de bepaling van de zelfontstekingsgrenzen van methaan, propaan en butaan mengsels bij verhoogde drukken tot 30 bar en voor verschillende concentraties. Het is aangetoond dat de zelfontstekingstemperaturen significant dalen bij verhoogde drukken. De alkaanmengsels die aanleiding geven tot de laagste zelfontstekingstemperaturen hebben een rijke brandstof/lucht verhouding, die eveneens afhangt van de initi¨ ele druk. De zelfontstekingsgrenzen van propaan/butaan mengsels komen goed overeen met de zelfontstekingsgrenzen van de component met de laagste zelfontstekingstemperatuur, namelijk n-butaan. De ligging van de zelfontstekingsgebieden kon eveneens het verloop van de bovenste explosiegrenzen bij verhoogde drukken en temperaturen van propaan en n-butaan mengsels verklaren. De numerieke studie concentreert zich op de modellering van de zelfontsteking van methaan/lucht mengsels bij verhoogde drukken. Eerst werd een nuldimensionale aanpak toegepast, die gebaseerd is op het model van Semenov. De chemie van de ontsteking is gemodelleerd door middel van gedetailleerde reactiemechanismen. Een methaan reactiemechanisme van de British Gas Corporation toonde de beste overeenkomst met de experimentele data. Om de thermische en massa diffusie en de natuurlijke convectie in rekening te brengen, werd een tweedimensionaal model opgebouwd met inbegrip van het reactiemechanisme. De warmteoverdracht en de natuurlijke convectie binnenin het gesloten volume worden gemodelleerd door middel van het CFD programma. De koppeling van de reactiekinetica met de stromingsmodellering resulteert in een nauwkeurige voorspelling van de zelfontstekingsgrenzen van methaan/lucht mengsels bij verhoogde drukken. Dit model is eveneens aangewend om de volumeafhankelijkheid van de zelfontstekingstemperatuur voor sferische en cilindrische vaten te onderzoeken.

List of symbols Latin Symbols A cp cv c B, C D EA EC ER F g h hi H L m M n n(t) P qc qd qr Q r R RR S SC SR t T T0

pre-exponential factor heat capacity at constant pressure heat capacity at constant volume concentration constants diameter activation energy conduction error radiation error view factor gravitational acceleration heat transfer coefficient specific enthalpy of species i enthalpy length mass molar mass (overall) reaction order number of chain carriers pressure convective heat flux conduction heat flux radiant heat flux heat release radius universal gas constant reaction rate surface area convective heat transfer area radiation heat transfer area time temperature initial temperature

ix

J kg−1 K−1 J kg−1 K−1 kg m−3 m J mol−1 K K – m s−2 W m−2 K−1 J kg−1 J m kg kg mol−1 – – kg m−1 s−2 J s−1 J s−1 J s−1 J m J mol−1 K−1 kg m−3 s−1 m2 m2 m2 s K K

x

List of symbols

Tc TG TJ TM Tw u v V W x X Y

critical temperature temperature of the gas temperature of the probe junction temperature of the probe stem temperature at the wall of the vessel internal energy per unit mass velocity volume molar mass spatial coordinate molar fraction mass fraction

K K K K K J kg−1 m s−1 m3 kg mol−1 m – –

Greek symbols α αth β βi δ J κ κM λ λair µ µb ν ρ σ φ Ψ τ τ0 ω˙

absorbance thermal diffusivity coefficient of thermal expansion temperature exponent Frank-Kamenetskii parameter mass fraction emissivity of the junction probe ratio of specific heats Planck mean absorption coefficient thermal conductivity excess air factor dynamic viscosity bulk viscosity kinematic viscosity density Stefan-Boltzmann constant equivalence ratio Semenov parameter time constant transmittance reaction or production rate

– m2 s−1 T−1 – – kg kg−1 – – – J s−1 m−1 K−1 – kg m−1 s−1 kg m−1 s−1 m2 s−1 kg m−3 J s−1 m−2 K−4 – – s – kg m−3 s−1

Dimensionless numbers Bi

Biot number

hL/λ

Nu

Nusselt number

hD/k

Pr

Prandtl number

ν/αth

Ra Re

Rayleigh number Reynolds number

βgL3 (Tcentre − Tw )/αth ν vD/ν

Contents Voorwoord

v

Abstract

vii

Korte samenvatting

viii

List of symbols 1 Introduction 1.1 The auto-ignition process 1.2 Gas explosions in industry 1.3 Aim and scope . . . . . . 1.4 Outline . . . . . . . . . .

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2 Background on auto-ignition 2.1 Factors influencing the auto-ignition temperature 2.1.1 Pressure . . . . . . . . . . . . . . . . . . . 2.1.2 Fuel type . . . . . . . . . . . . . . . . . . 2.1.3 Fuel concentration . . . . . . . . . . . . . 2.1.4 Volume of the test vessel . . . . . . . . . . 2.1.5 Material effect . . . . . . . . . . . . . . . 2.1.6 Auto-ignition criterion . . . . . . . . . . . 2.2 Experimental determination of the AIT . . . . . 2.2.1 Standardised test methods . . . . . . . . . 2.2.2 Experimental methods . . . . . . . . . . . 2.3 Auto-ignition theories . . . . . . . . . . . . . . . 2.3.1 Chain spontaneous ignition . . . . . . . . 2.3.2 Semenov theory of thermal ignition . . . . 2.3.3 Frank-Kamenetskii theory . . . . . . . . .

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3 Experimental set-up and procedures 3.1 Experimental set-up . . . . . . . . . . 3.1.1 Mixture preparation equipment 3.1.2 Buffer vessel . . . . . . . . . . 3.1.3 Explosion vessel . . . . . . . .

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Contents

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37 38 41 47

4 Experimental results: 4.1 Auto-ignition limits at atmospheric pressure . . . . . 4.2 Auto-ignition limits of propane/air mixtures . . . . . 4.3 Auto-ignition limits of butane/air mixtures . . . . . 4.3.1 Auto-ignition limits of n-butane/air mixtures 4.3.2 Auto-ignition limits of i-butane/air mixtures 4.3.3 Auto-ignition limits of LPG/air mixtures . . 4.4 Comparison between the AIT and the UFL . . . . . 4.5 Auto-ignition limits of methane/air mixtures . . . .

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49 50 51 55 55 58 58 62 64

5 Numerical study of the auto-ignition 5.1 Numerical method . . . . . . . . . . . . . . . . 5.1.1 Background on auto-ignition modelling 5.1.2 Mathematical model . . . . . . . . . . . 5.1.3 Reaction mechanisms . . . . . . . . . . 5.1.4 0-D model . . . . . . . . . . . . . . . . . 5.1.5 1-D and 2-D CFD-Kinetics model . . . 5.1.6 Auto-ignition criterion . . . . . . . . . . 5.2 Numerical results of methane/air mixtures . . . 5.2.1 0-D model . . . . . . . . . . . . . . . . . 5.2.2 1-D model . . . . . . . . . . . . . . . . . 5.2.3 2-D model . . . . . . . . . . . . . . . . . 5.2.4 Discussion . . . . . . . . . . . . . . . . . 5.3 Numerical results of propane/air mixtures . . .

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3.2 3.3 3.4

3.1.4 Data acquisition . . . . . . . . . . . . . Experimental procedure . . . . . . . . . . . . . Analysis of the temperature measurement error Fuel Type . . . . . . . . . . . . . . . . . . . . .

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6 Influence of the vessel size on the AIT 6.1 Models for the volume dependency of the auto-ignition ature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Model evaluations for spherical vessels . . . . . . . . . 6.3 Model evaluations for vertical cylindrical vessels . . . . 6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . .

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96 97 101 102

7 Conclusions and recommendations 105 7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 7.2 Recommendations for further research . . . . . . . . . . . . . . 107 A Test results

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B Chemical kinetics mechanism

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Nederlandse samenvatting

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Contents

xiii

Bibliography

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Curriculum vitae

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List of publications

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xiv

Contents

Chapter 1

Introduction Life is a flame that is always burning itself out, but it catches fire again every time a child is born. George Bernard Shaw, Irish literary Critic, Playwright and Essayist (1856 – 1950)

S ince ancient times, people consider a flickering flame a charming mystery. Fire is one of the basic elements of the world. For thousands of years people have

made use of it. It has been the object of curiosity and scientific investigation. Fire or combustion can be of great benefit, but it can also cause severe damage if it occurs uncontrolled. Many chemical processes use combustible gases and vapours at elevated pressures and high temperatures. In order to evaluate the auto-ignition hazard and to ensure the safe and economic operation of these processes, it is important to obtain knowledge about the influence of the process conditions on the lowest possible temperature at which spontaneous ignition takes place.

1.1

The auto-ignition process

Fire or combustion is a chemical reaction in which a fuel reacts with oxygen and heat is released. The well-known fire triangle (Figure 1.1) represents the three prerequisites that are needed for a fire: the fuel (1), the oxidiser (2) and heat (3). If one of these conditions is missing, fire does not occur or a fire can be extinguished if one condition is removed. The fuels that are used in this study are the low alkanes, such as methane, propane and butane. The oxidiser used in this study is air but can also be pure oxygen, chlorine (gas), bromine (liquid) or sodium bromate (solid). The lower and the upper concentration values of a combustible gas within which a flame is able to propagate are called the flammability limits. Outside these limits the gas mixture is non-flammable. It should be taken into account that these flammability limits are depending on

1

2

FIRE

y

Ox

erg En

idi ser

Chapter 1 Introduction

Ignition Source Spontaneously, without Ignition Source

Fuel Figure 1.1: The fire triangle.

temperature and pressure and that these limits do not apply for auto-ignition reactions. The third condition of the fire triangle is a source of heat. Usually this is an ignition source, such as a spark or a flame. A second way to ignite a gas mixture is to heat it up until it ignites spontaneously. This process is called a spontaneous ignition or an auto-ignition. The auto-ignition temperature (AIT) of a gas mixture is the minimum temperature at which a mixture of a fuel and an oxidiser ignites spontaneously without ignition source. The AIT values of hydrocarbon-air-mixtures found in literature are usually determined according to standard test methods in small vessels and at atmospheric pressure (e.g. EN 14522, DIN 51 794, ASTM E 659–78 and BS 4056–66). The auto-ignition temperature is, however, not constant but dependent on, for example, the following factors: pressure, volume of the vessel and flow conditions. In industry, gas mixtures are present at high pressures and large volumes. Consequently, the standardised AIT values are often not directly applicable to industrial conditions. Although the auto-ignition process is very complex, some trends caused by changes in process conditions can be predicted using a simple representation of the auto-ignition process. The auto-ignition is a balance between the heat production and the heat loss. If the rate of heat production is higher than the rate of heat loss, the temperature of the gas mixture will increase and an auto-ignition is likely to occur. An increase of pressure increases the rate of heat production more than the rate of heat loss, which causes the ignition temperature to decrease. Increasing the flow and the turbulence will increase the heat loss, which make the auto-ignition more difficult to occur. Consequently the auto-ignition temperature will increase with increasing flow and turbulence. These influences will be described into more detail in section 2.1. The following paragraphs will describe two other auto-ignition processes that can occur. Auto-oxidation or self heating is a slow oxidation process that can result into an ignition if the heat cannot be dissipated adequately. The process of self-heating is similar to the auto-ignition process. It is a balance between the

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1.2 Gas explosions in industry

Gas processing plants

1987-1991 1992-1996 1997-2001

Petrochemical plants

Refinery plants

0

50

100

150

200

250

300

350

Number of accidents

Figure 1.2: Evolution of large accidents outside the USA (Marsh, 2003).

heat production due to the chemical reactions and the heat loss. Self-heating can occur if materials are handled in driers or with materials stored in piles. A well known example is the spontaneous combustion of coal piles stored on the ground. Investigating the auto-ignition process is not only of interest for the identification of hazards, it can also be of benefit in combustion systems, such as diesel engines. This ignition is called a compression ignition. Adiabatic compression results in high temperatures according the following equation: T2 P2 (κ−1) =( ) κ T1 P1

(1.1)

where subscripts 1 and 2 refer to the initial and final state, T is the absolute temperature and P is the absolute pressure and κ is the ratio of the specific heats. Consequently by means of compression the temperature can be increased above the auto-ignition temperature to cause an auto-ignition.

1.2

Gas explosions in industry

Over the last 20 years there has been an increased emphasis on gas explosion safety because of a number of serious accidents. In spite of the improvement of the safety management and technological development a lot of accidents still occur and take away human lives or cause huge financial losses. As can be seen from figure 1.2 the number of large accidents outside the United States remains high. The number of incidents in refinery plants and gas processing plants has even increased in the period from 1997 to 2001 compared to the previous years.

4


Table 1.1 shows the property damage losses and casualties for some of the major accidents in the (petro)chemical industry over the past 40 years. The losses are the direct damage losses and do not include additionally production loss, down time, employee injuries and fatalities, and legal or environmental penalties. The ratio of the total cost of the accident to the direct property damage costs can be a factor of 2 to 5 according to Pekalski (2004). These incidents demonstrate the horrific consequences of explosions with methane, propane or butane and of explosions caused by auto-ignitions. These accidents caused many deaths and huge financial losses. It is vital that process safety has a high priority in the design and operation of chemical plants. Engineers must be able to identify and estimate the explosion hazard in order to take preventive and protective measures. Many explosion data, such as explosion limits, minimum ignition energies and auto-ignition temperatures can be found in standard texts or databases. In spite of this large amount of data, unwanted explosions still occur. One of the reasons is that most of these data are determined at atmospheric pressure and ambient conditions, while most industrial processes operate under different conditions. These changes in process conditions strongly affect the values of the explosion data. For example, the auto-ignition temperature is significantly influenced by changes in process conditions, such as increased pressure, increased volume and flow conditions. Therefore large safety margins are needed in order to apply the standardised auto-ignition temperatures to industrial processes. A poor knowledge of the influence of the different process conditions can lead to unsafe situations as well as to non-economic situations. A profound study of the phenomena that lead to auto-ignition is indispensable for a safer and more economical design of process installations.

1.3

Aim and scope

In literature a large amount of auto-ignition data is available on gas mixtures at atmospheric pressure. Auto-ignition experiments at elevated pressures are, however, scarce and the volumes in which the auto-ignition temperatures are determined are small (0.5 up to 1 litre). Little information is available on the auto-ignition temperature of mixtures of different fuels. It can be concluded that the available auto-ignition data concerning the composition of the gas mixtures, the pressure and the volumes of the test vessels are limited. Concerning the numerical simulation of the auto-ignition process there is still a lot of work to perform. There only exist a few models (Semenov (1935), Frank-Kamenetskii (1955) and Shell Global Solutions (2001)) for the determination of the auto-ignition temperature. These models contain simplified assumptions for the heat production inside the gas mixture and for the heat loss to the surroundings. This implies that the applicability of these models is very limited. Besides this shortcoming these models are only validated by experiments at atmospheric pressure and in small volumes. The question should be put whether these models are able to predict the auto-ignition temperature

Feyzin, France Umm Said, Qatar Texas City, USA Good Hope, LA, USA Mexico City, Mexico Ft. McMurray, Canada Antwerp, Belgium Antwerp, Belgium Pasadena, TX, USA Warren, PA, USA Yokkaichi, Japan Martinez, California, USA Yokkaichi, Japan Thessaloniki, Greece Aruba Geleen, Netherlands

1966 1977 1978 1979 1984 1984 1987 1989 1989 1990 1996 1997 1997 1999 2001 2003

storage gas plant storage tank barge storage refinery petrochemical petrochemical petrochemical petrochemical refinery refinery refinery refinery refinery chemical

plant type propane LPG LPG butane LPG light gas oil ethylene oxide ethylene oxide isobutane LPG fuel oil light gas oil fuel oil light gas oil oil natural gas

substance a

BLEVE fire BLEVE fire ball BLEVE auto-ignition explosion explosion VCE explosion, fire auto-ignition auto-ignition auto-ignition auto-ignition auto-ignition auto-ignition

event type b

$ 85,000,000 $ 172,000,000 $ 115,000,000 $ 20,000,000 $ 29,000,000 $ 109,000,000 Unknown $ 99,000,000 $ 869,000,000 $ 32,000,000 $ 750,000 $ 22,000,000 $ 900,000 $ 43,000,000 $ 134,000,000 Unknown

property damage loss 18/81 7/13+ 7/10 12/25 650/6400 0/0 0/14 32/11 23/314 Unknown 0/0 0/0 0/4 0/0 0/0 3/2

casualties (deaths/injuries)

Table 1.1: Examples of some major disasters with methane, propane or butane and disasters which are caused by an auto-ignition obtained from Lees (1996), Marsh (2003), the MARS database and the JST failure knowledge database. / a BLEVE stands for boiling liquid expanding vapour explosion and VCE stands for vapour cloud explosion, b The losses are stated in January 2002 US dollars.

location

year

1.3 Aim and scope 5

6


at elevated pressures and other process conditions with sufficient accuracy. It can be concluded that both on a theoretical and an experimental level further research is necessary in order to determine the influence of the different process conditions on the auto-ignition temperature of different gas mixtures. Therefore this study aims to accomplish the following objectives: • Firstly, the pressure and concentration dependence of the auto-ignition temperature will be determined experimentally for different gas mixtures. These experiments are conducted inside an 8 litre explosion vessel at pressures up to 3 MPa and temperatures up to 720 K. The combustible gases that will be studied are methane (CH4 ), propane (C3 H8 ), n-butane (C4 H10 ) and i-butane (C4 H10 ). First the auto-ignition limits are determined for the separate components. Thereafter two LPG (Liquefied Petroleum Gas) mixtures will be tested to investigate the influence of the different components on the auto-ignition limits of the mixture. • Secondly, a numerical model will be developed in order to describe the thermo-chemical process of the auto-ignition and to calculate auto-ignition temperatures at real process conditions. The auto-ignition model will focus on the heat production by the comparison of different reaction mechanisms that describe the chemical kinetics. A second focus will be on the heat loss. Firstly the heat loss will be modelled by a zero- or onedimensional model. Thereafter the heat loss will be modelled more accurately by means of computational fluid dynamics. This technique also allows to model the auto-ignition process under real process conditions.

1.4

Outline

In Chapter 2 a theoretical background is given. First an overview of process conditions that affect the auto-ignition temperature is given. Secondly, a large number of existing standards for the determination of the auto-ignition temperature are compared in order to find their shortcomings and to draw lessons for the new operating standard of this study. Finally, three auto-ignition theories will be described in detail. These theories will be used in the numerical model of this study (Chapter 5). Chapter 3 describes the experimental set-up and procedures that are used in this study to determine the auto-ignition temperature. An analysis of the temperature measurement error is given at the end of this chapter. Chapter 4 presents the experimental results of the auto-ignition limits at atmospheric and at elevated pressures. At first the results are given for propane/air, n-butane/air and i-butane/air mixtures. Thereafter the auto-ignition limits of two LPG (Liquefied Petroleum Gas) mixtures are compared with the autoignition limits of the separate fuels. The last part of the experimental study focuses on the auto-ignition limits of methane/air mixture. The concentration and pressure dependence and the reproducibility of the determination of the auto-ignition limit is investigated extensively.

1.4 Outline

7

Chapter 5 describes first the numerical methods that are used in this study to determine the auto-ignition temperature. Thereafter in section 5.2 the numerical results of the auto-ignition limits for methane/air mixtures are presented and compared with the experimental results. In Chapter 6 the influence of the volume on the auto-ignition temperature will be investigated numerically by the application of the numerical model developed in this study. Finally, the auto-ignition temperatures in spherical volumes are compared with the AIT in cylindrical volumes.

8


Chapter 2

Background on auto-ignition Murphy’s Law about Thermodynamics: Things get worse under pressure! anonymous

F irst an overview is given of the factors that influence the auto-ignition temperature, such as pressure, fuel type, fuel concentration, volume and autoignition criterion. Before describing the experimental apparatus and procedure applied in this work, it is important to review the different methods available for the determination of the auto-ignition temperature. Therefore the standardised methods are presented and compared. Subsequently, the principal experimental methods, which have been used to investigate auto-ignition, will be described. Finally, three ignition theories of chain and thermal ignition on which the numerical model of this study is built, are described.

2.1

Factors influencing the auto-ignition temperature

The auto-ignition of a gas mixture is a complex phenomenon influenced by many factors. The parameters which play an important role can be subdivided into three categories: the mixture parameters, secondly the parameters which are dependent on the test apparatus and finally the parameters which are dependent on the test method: • The mixture parameters: pressure, fuel type, fuel concentration, influence of additives and oxidiser. • Test apparatus parameters: volume of the test vessel, material effect of the test vessel and flow. • Test method parameters: auto-ignition criterion.

9

10

Chapter 2 Background on auto-ignition

This section will only treat the factors which are investigated for this thesis. These are the pressure, fuel type, the fuel concentration, the volume of the test vessel, the material effect and the auto-ignition criterion.

2.1.1

Pressure

An increase in pressure generally decreases the auto-ignition temperature of a gas mixture. Since many processes in the chemical industry are conducted at elevated pressure, it is important to have knowledge of the pressure dependence of the auto-ignition temperature. Several hydrocarbon fuels obey Semenov’s equation (see also Section 2.3.2) over a limited pressure range (Zabetakis et al., 1965): EA Pc +C (2.1) ln( ) = T0 2RT0 where Pc and T0 are the initial pressure and temperature at the critical condition, EA is the activation energy of the applied Arrhenius reaction, R is the universal gas constant and C is a constant depending on different factors including the surface/volume ratio of the vessel and the heat transfer coefficient. A main difficulty to obtain the pressure dependency of the auto-ignition temperature is the determination of the activation energy. This activation energy is not only dependent on the fuel mixture, but also on the pressure and the temperature at which the reactions occur. This activation energy can be determined experimentally by means of measurements of the ignition delay time or the rate of temperature rise. These measurements are time-consuming and it is difficult to represent the industrial conditions, such as volume and pressure by means of an experimental set-up. Since the auto-ignition temperature decreases with increasing pressure, the auto-ignition temperatures determined by the standardised methods, which are generally determined at atmospheric pressure, should not be used to assess the auto-ignition risk at elevated pressure. Accordingly, further research and the experimental determination of autoignition temperatures at elevated pressure is necessary if the auto-ignition risk of industrial processes at elevated pressure needs to be assessed.

2.1.2

Fuel type

The auto-ignition temperature is strongly dependent on the fuel type. As can be seen from table 2.1 the auto-ignition temperature for hydrocarbon/air mixtures decreases with increasing molecular weight and increasing chain length. The auto-ignition temperature is also higher for branched chain hydrocarbons than for straight chain hydrocarbons. The auto-ignition temperature of i– butane is almost 100K higher than the auto-ignition temperature of n–butane, as can be seen from table 2.1. This behaviour can be explained qualitatively because for the branched i–butane a higher activation energy is needed to distract a CH3 -radical than for the straight n–butane. Zabetakis et al. (1965) discovered that the auto-ignition temperature of pure components obtained in a 200 ml Erlenmeyer flask according to the ASTM standard can be correlated

2.1 Factors influencing the auto-ignition temperature

AIT [K] 868 788 743 733 638 533 503

11

Fuel methane ethane propane i–butane n–butane pentane hexane

Table 2.1: Summary of the auto-ignition temperatures (AIT) of alkane/air mixtures according to the Chemsafe (2006) database.

to the average carbon chain length Lave , defined as: P 2 gi Ni Lave = M (M − 1)

(2.2)

where gi is the number of possible chains, which contain Ni carbon atoms and M is the number of methyl groups. The auto-ignition temperatures of 20 hydrocarbons are plotted as a function of the average carbon chain length on figure 2.1. The gases that are used in this thesis are low hydrocarbons, such as methane, propane, n–butane and i–butane. The addition of components with a lower auto-ignition temperature to a mixture decreases the auto-ignition temperature of the mixture. An inaccurate prediction of the auto-ignition temperature for a fuel mixture is the auto-ignition temperature of the component with the lowest AIT. A more precise prediction for the auto-ignition temperature of alkane/air mixtures is a linear empirical correlation given by Ryng (1985): X AITmix = Xi AITi (2.3) where Xi is the molar fraction of component i and AITi is the auto-ignition temperature of component i. Some additives can also promote the auto-ignition behaviour of an alkane/air mixture although they themselves might have a higher auto-ignition temperature. For example, the addition of small amounts of ammonia lowers the auto-ignition temperature of a methane/air mixture (Caron et al., 1999). This promotion effect of ammonia has been researched numerically by the author of this thesis but will not be treated in this text. Further information about this study can be found in (Norman et al., 2007) and (Van den Schoor et al., 2008).

2.1.3

Fuel concentration

The concentration most sensitive to auto-ignition is generally not the stoichiometric concentration. The lowest auto-ignition temperature occurs at a richer concentration between the stoichiometric concentration and the upper flammability limit (Bartknecht, 1993). This is schematically shown in figure

12


Figure 2.1: The auto-ignition temperatures of hydrocarbon/air mixtures as a function of the average carbon chain length (Zabetakis et al., 1965).

2.2. Methane/air mixtures constitute an exception to this rule according to measurements of Kong et al. (1995). The lowest auto-ignition temperature for methane/air mixtures occurred in the lean range of 3.0–8.0 mol% CH4 , while the stoichiometric concentration is 9.5 mol% CH4 . In this thesis the dependence of the fuel concentration on the auto-ignition will be researched for the low alkane/air mixtures. Therefore different concentrations varying from lean to rich mixtures will be tested in order to find the concentration with the lowest auto-ignition temperature.

2.1.4

Volume of the test vessel

The auto-ignition temperature decreases with increasing vessel size. This volume dependency can be determined by the Semenov model, see Section 2.3.2. For spherical vessels this model results in the following relationship between the pressure and the gas temperature at auto-ignition (see equation 2.41): ln(

Pc EA C )= + ln( √ ) T0 2RT0 D

(2.4)

The experimental determination of the auto-ignition temperature is characterised by the small volume of the test vessel (Section 2.2.1). On the other hand, most of the industrial processes involve large vessel volumes. Therefore knowledge of the volume dependency of the auto-ignition temperature is

2.1 Factors influencing the auto-ignition temperature

Fuel concentration

Saturated vapour/air mixtures Upp

mm er fla

abilit

y lim

it

Autoignition zone

Flammable mixtures Mists

Lower flammabilit

13

y limit

Temperature

AIT

Figure 2.2: A typical flammability diagram

indispensable for the industrial safety. In Chapter 6 this dependency will be researched numerically in detail.

2.1.5

Material effect

Besides the volume of the test vessel, there is an influence of the material of the test vessel on the auto-ignition temperature. The material surfaces can promote as well as inhibit the ignition because they can: • create or destruct active radicals • act as a heat source or heat sink • modify the mass transport • adsorb intermediary products The material effect is more distinct for the auto-ignition at hot surfaces and for gases with high auto-ignition temperatures. Frank and Blackham (1952) reported that a change in the metal surface had no consequence when the autoignition temperatures was below 290 ◦ C. Coward and Guest (1927) investigated the ignition over heated metal strips of natural gas. Catalytic surface such as platinum had the highest hot surface ignition temperatures (1150 ◦ C up to

14


1400 ◦ C) and the ignition temperature lowered by 100-150 ◦ C if a stainless steel surface was applied. Smyth and Bryner (1997) also observed differences between the ignition temperatures of alkanes at nickel, steel and titanium surfaces. The highest temperatures were observed for the nickel surface, while the lowest were for the stainless steel surface and the values for titanium surface were intermediate. Hilado and Clark (1972) investigated the effect of ferric oxide powder on the auto-ignition temperature of organic compounds. They found that the autoignition temperatures decreased if the organic compounds were in contact with rusty iron or steel. This effect was only observed for the organic compounds with an auto-ignition temperature above 290 ◦ C. The material effect is important for chemical industries because different materials can be present in the process installations. It is also possible that catalytic material may spread unknowingly throughout the process equipment. It is concluded that the auto-ignition temperature of organic compounds can be significantly affected by the different materials if the auto-ignition temperature is above 290 ◦ C.

2.1.6

Auto-ignition criterion

The most commonly used auto-ignition criterion is the visual observation of a flame (see section 2.2.1). Other methods are temperature or pressure measurements and the analysis of the reaction products. A first disadvantage of the visual observation is that it can not be used for the detection of invisible flames of e.g. hydrogen. A second disadvantage is that this method is only applicable if the test set-up has visual access and no soot formation occurs. At elevated pressure it is more difficult to obtain visual access. Therefore temperature and pressure measurements can replace the visual criterion. It is important to have an adequate criterion of the temperature and pressure rise. A change of the temperature rise criterion from 50 K to 200 K can have a major influence on the auto-ignition limit. The analysis of the reaction products is often time consuming and expensive. It is also difficult to determine by means of reaction products analysis if auto-ignition has occurred. This thesis focuses on finding an appropriate auto-ignition criterion for the experiments conducted at high pressure.

2.2

Experimental determination of the AIT

The auto-ignition temperature of a gas mixture is influenced by many factors. Therefore it is difficult to standardise a determination method. A large number of standards exist, which will be discussed in the following paragraph. Furthermore many researchers use an experimental set-up which is adapted to their specific situation. The differences in the auto-ignition temperature of methane determined by different test methods are presented in table 2.2. As can be seen from this table, the auto-ignition temperature of methane is not a constant value, but depends

2.2 Experimental determination of the AIT

AIT [K] 793 810 813 813 868 890 893 913 923

Test method standard DIN 14011 NFPA (1951) standard ASTM D-2155 NFPA-325M standard DIN 51794 0.8/1 dm3 closed cylindrical vessel standard EN 14522 1 dm3 closed cylindrical vessel DIN 14011

15

Reference Freytag (1965) Zabetakis et al. (1954) Coffee (1980) Affens and Sheinson (1980) Chemsafe (2006) Reid et al. (1984) This study (Section 4.1) Kong et al. (1995) Affens and Sheinson (1980)

Table 2.2: Comparison of the auto-ignition temperature (AIT) of methane/air mixtures determined by different test methods at atmospheric pressure.

on the test method. The following paragraph will discuss and compare the different standardised test methods. Paragraph 2.2.2 will describe the principal experimental methods which have been used to investigate auto-ignition.

2.2.1

Standardised test methods

There exists a large number of standards for the determination of the autoignition temperature at atmospheric pressure, e.g. EN 14522, DIN 51 794, IEC 60079–4, ASTM D2155–66, ASTM E 659–78 and BS 4056–66. Each of these standards makes use of a similar set-up. Therefore only the European Standard EN 14522 will be described in detail. Afterwards the differences between the standards will be described. ASTM D2883–95 is the only standard which can be used for the determination of the auto-ignition temperature at high pressure for liquids and solids. Unfortunately no standardised method exists for the auto-ignition temperature at high pressure of gases. Therefore a new operating procedure will be developed in this thesis. The European Standard EN 14522, approved on 1 August 2005, is intended for the determination of the auto ignition temperature of gases and vapours at ambient pressure up to temperatures of 923 K. The standard test apparatus consist of a 200 ml Erlenmeyer flask of borosilicate glass positioned in an electrically heated hot-air oven (Figure 2.3). Two thermocouples T1 and T2 are used to measure and to control the temperature of the flask. The fuel gases are introduced by means of a removable filling tube and the flow rate should be 25 ± 5 ml/s. In case of liquid fuels, the liquid is supplied by a syringe, which can produce droplets having a volume of 25 ± 10 µl. The test shall be classified as an ignition if any visible flame is observed via the mirror within 5 minutes after introducing the substance. Because of the visible ignition criterion the apparatus shall be positioned in a darkened room. The auto-ignition temperature is the lowest temperature at which an ignition of a flammable gas or flammable vapour in mixtures with air or air/inert gas occurs. This limit is determined by varying the temperature of the test vessel and the amount of

16


Mirror T1

Test vessel Hot-air oven T2 Figure 2.3: Test apparatus for the determination of the auto ignition temperature according to the EN 14522.

flammable substance. The other standards for the determination of the auto-ignition temperature at atmospheric pressure are based upon on the same principle of injecting a liquid or a gas in a hot open reservoir. A summary of the existing standards is given in table 2.3. The majority of the standards makes use of a 200 ml erlenmeyer made of borosilicate glass. Only in the IEC 60079–4 and the BS 4056–66 standard it is described that other materials like quartz or metal can be used for special conditions. The ASTM E 659–78 (1989) standard prescribes the use of a round bottomed vessel of 500 ml instead of a 200 ml erlenmeyer. Because a larger volume lowers the auto-ignition temperature (see section 2.1.4), it is expected that ASTM E 659–78 (1989) results in lower auto-ignition temperatures. Every standard at atmospheric pressure prescribes a visual criterion for the detection of an auto-ignition. Only the ASTM E 659–78 (1989) and the EN 14522 (2005) standards draw a distinction between a cool flame temperature and a hot flame temperature. The maximum induction period at which the flask is observed until ignition occurs, differs from 5 for most standards to 10 minutes for the ASTM E 659–78 (1989) and ASTM D 2883–95 (1995) standard. These standards also include the observation of cool flame phenomena. There exists only one standard for the determination of auto-ignition temperatures of liquids and solids at pressures above 1 atm, namely ASTM D 2883–95 (1995), which can be used for pressures from low vacuum up to 0.8 MPa. This standard prescribes the use of a closed steel spherical vessel with


17

a volume of 1 dm3 . A standard ampoule with 0.2 ml of the testing sample is inserted in the closed vessel. The ampoule is opened through the activation of an electromagnet, which releases the sample. There is no visual criterion since the closed vessel has no optical access. The temperature and pressure are recorded for a minimum of 10 minutes. The cool flame and hot flame reactions are detected by the evolution of heat that raises the temperature and the pressure. There are no quantitative criteria based on a temperature or a pressure rise for the cool flame and hot flame temperature. The standard describes the different types of reactions by means of illustrations of the temperature profiles. Pre-flame reactions can last hundreds of seconds and have a temperature increase of about 10 K. Cool flame reactions have a duration of the order of hundred seconds and a maximum temperature increase of 50 K, while hot flame reactions are rapid reactions with a typical duration of less than 25 seconds and a temperature rise from 80 K to 200 K. To summarize, many standards thus exist for the determination of the autoignition temperature. They have several similar limitations: • The auto-ignition temperatures of gases can only be determined at atmospheric pressure. There exists only one standard for the determination of liquids and solid at a pressure up to 0.8 MPa. • The concentrations cannot be verified and the mixing with air is not homogeneous. • Most of the standards use a borosilicate erlenmeyer and the influence of other materials on the auto-ignition temperature is not examined. • No procedure exists for oxygen enriched or oxygen depleted mixtures. • There is no preheating of the fuel. • Most standards only have a visual criterion without temperature measurements. • Almost all set-ups are open cup systems in which volatile components can easily evaporate and disappear from the system. • The test vessels are small compared to industrial installations and since the auto-ignition temperature decreases with increasing volume, it is important to have knowledge about the volume dependency. The new operating procedure for the experiments of this thesis will answer some of the previous shortcomings: • The auto-ignition temperatures of gases will be determined at elevated pressure. • The fuel concentrations will be verified and the mixing with air will be homogeneous.

DIN 51 794 p = 1 atm T ≤ 923 K gases/vapours borosilicate erlenmeyer V = 200 ml open visual flame t ≤ 5 min

EN 14522

p = 1 atm T ≤ 923 K gases/vapours borosilicate erlenmeyer V = 200 ml open visual flame t ≤ 5 min gases/vapours borosilicate/quartz/ metal erlenmeyer V = 200 ml open visual flame t ≤ 5 min

p = 1 atm

IEC 60079–4 p = 1 atm T ≤ 923 K gases/vapours borosilicate/quartz/ metal erlenmeyer V = 200 ml open visual flame t ≤ 5 min

BS 4056–66

liquids borosilicate erlenmeyer V = 200 ml open visual flame t ≤ 5 min

p = 1 atm

ASTM D2155–66

liquids borosilicate round bottomed V = 500 ml open visual flame t ≤ 10 min

p = 1 atm

ASTM E 659–78

ASTM D2883–95 p ≤ 0.8 MPa T ≤ 923 K liquids/solids steel explosion vessel V =1l closed temp./press. recordings t ≤ 10 min

Table 2.3: Comparison between standardised methods for the determination of the auto-ignition temperature.

auto-ignition criterion time criterion

test vessel

scope

method

18 Chapter 2 Background on auto-ignition


19

• The auto-ignition criterion will be based on temperature and pressure measurements. • The vessel used in this study, as can be seen in section 3.1, has a volume of 8 litres which is large in comparison with the volumes applied in the standardised methods.

2.2.2

Experimental methods

Next to the standardised set-ups, a number of experimental methods exist which have been used to investigate auto-ignition. These experimental methods can be subdivided into four categories: • Unstirred and stirred closed vessels The unstirred set-up resembles the standardised methods. The major difference is that the vessel is not open, but closed. An advantage of this method is that auto-ignition experiments can be conducted at elevated pressures. This method has been used widely by researchers, such as Melvin (1966), Reid et al. (1984), Kong et al. (1995), Chandraratna (1999) and Pekalski et al. (2005). A disadvantage of the closed static vessel is the asymmetric gradient in temperature that arises from the natural convection because of the self-heating of the gas. Only at extremely low gas densities or in micro-gravity environment (Foster and Pearlman, 2006) the effect of the buoyancy is small and can be neglected. An alternative way to reduce the effect of buoyancy, developed by Griffiths et al. (1974) and Reid et al. (1984), is to incorporate a mechanical stirrer in the closed vessel. The temperature distribution will be more homogeneous because of the higher convection. Since the stirring improves the heat transfer at the wall, it is expected that the auto-ignition temperature will increase. The disadvantages of these systems are the long injection time, heating time and stagnation time of the mixture. These disadvantages make this technique not suitable for experiments with a small ignition delay time, which is the time lag between the injection of the test mixture and the moment of auto-ignition. The long injection and the long heating time cause a significant uncertainty about the ignition delay time. • Rapid compression machines Auto-ignition may also be brought about by adiabatic compression in a Rapid Compression Machine (RCM). The rapid heating of the gas mixture is caused by the mechanical compression ahead of a piston. This technique was applied by Griffiths et al. (1994), Minetti et al. (1995), Westbrook et al. (1998) and Tanaka (2003). Contrary to the closed vessel set-up, the temperature of the cylinder wall of the combustion chamber is far from the auto-ignition temperature. In order to minimise the heat loss, the compression must be conducted very rapidly. Therefore the RCM is well suited to investigated auto-ignitions at high pressures with very small timescales. However, this process is not fully adiabatic because

20


of the high pressures, high temperature gradients and considerable fluid motions (Griffiths and Hasko, 1984). This system is commonly adopted for the determination of the auto-ignition behaviour of engine fuels. • Shock Tubes A third method to ignite a fuel mixture is by a shock wave. In a shock tube arrangement a diaphragm initially separates a high and a low pressure chamber. By the instantaneous bursting of the diaphragm a shock wave is generated which propagates through the low pressure chamber. If the chamber is filled with the fuel mixture, the reactants are heated and compressed instantly. This method is applied by Burcat et al. (1971), Brown and Thomas (1999) and Petersen et al. (1999). The advantage of this technique is the short heating time to reach temperatures up to 5000 K. Therefore this technique is mainly applied for auto-ignition tests with very low induction times. • Continuous flow apparatus The last type of experimental apparatus consists of the continuous flow devices, such as the well-stirred flow reactor and the flow tubes. The wellstirred flow reactor was developed first by Longwell and Weiss (1955). In the Longwell jet-stirred reactor the reactants are centrally injected into a spherical chamber through a perforated tube. These reactants ignite at some distance from the injection point, depending on the temperature and the flow conditions. The products exit through outlets at the sphere wall. The occurrence of auto-ignition is determined by the observation of a flame or a rapid increase of the temperature at the flame front. The kinetics of the oxidation can be followed by means of gas chromatography analysis. This type of jet-stirred reactors was also applied at elevated pressures by Lignola et al. (1989) and Dagaut et al. (1991). An alternative way to ignite a reactant mixture is in a heated tube under laminar flow conditions (Griffiths and Scott, 1987). In this set-up the ignition occurs not in time but in space. For example, a two stage ignition is observed as a spatial separation of a cool flame followed downstream by a hot flame area. The kinetics of the oxidation can be measured by probe sampling and gas chromatography analysis or by the spectroscopy of the chemiluminescent emissions.

2.3

Auto-ignition theories

The auto-ignition process can be considered as a thermal explosion or as a chemical/chain explosion. For the thermal explosion theories, the auto-ignition is considered a consequence of the imbalance between the heat production because of the chemical reactions in the gas mixture and the heat loss to the surroundings. If the heat production is greater than the heat loss, the temperature of the gas mixture will increase and an explosive condition arises. In the

2.3 Auto-ignition theories

21

Figure 2.4: Reaction path.

opposite case, as long as the heat loss can keep pace with the heat production thermal explosion is impossible. The critical condition is achieved when the heat release equals the heat loss. The chemical or chain auto-ignition theory investigates the auto-ignition starting from the chemical reactions and in particular the chain reactions that take place during the auto-ignition. Although chemical auto-ignition cannot be separated from thermal auto-ignition, because both processes take place simultaneously, first the chemical or chain spontaneous ignition will be described and thereafter the thermal ignition theories of Semenov (1935) and FrankKamenetskii (1955) will be described. Semenov (1935) was the first to describe the theory of thermal ignition in an analytical form. Later Frank-Kamenetskii (1955) extended the model to a one-dimensional one.

2.3.1

Chain spontaneous ignition

Chemical reactions occur when molecules of one species collide with other molecules. As a consequence one or more new molecules are formed. Detailed chemical kinetics are frequently used to describe the transformation at molecular level of reactants into products. For example, the oxidation of methane can be described by the global reaction: CH4 + 2O2

A

CO2 + 2H2 O

This reaction however does not happen like this at the molecular level. The oxidation of methane actually consists of hundreds of elementary chain reactions with tens of species. An example of a reduced mechanism for the low temperature oxidation of methane of Reid et al. (1984) is shown in figure 2.4. Chain branching occurs when created radicals in their turn react with other

22


species to form more radicals. These radicals are called the chain carriers. The amount of chain carriers n(t) generally changes as follows: dn(t) = k · n(t) + I dt

(2.5)

The solution of this equation is: n(t) = (n(t0 ) +

I kt I )e − k k

(2.6)

or for n(t0 ) = 0: I n(t) = ( )(ekt − 1) k

(2.7)

where t is the time and t0 is the initial time and I is the rate constant of the chain initiating reactions. If k > 0 the number of carriers will increase exponentially and radical chain explosion occurs. If k < 0 which means that the rate constant for the chain termination is higher than that for the chain carrier branching, the solution of equation 2.5 is, denoting that j ≡ −k: I n(t) = ( )(1 − e−jt ) j

(2.8)

The number of carriers will asymptotically approach I/j at steady state. This is a slow oxidation process. The critical point is consequently when k ∼ = 0. For a system with hundreds of reactions, k is an average over all reactions taking place. It is also referred to as the net branching factor φ. The group of elementary reactions can be subdivided into four categories: chain initiating, propagating, branching or terminating reactions depending on their contribution to the net branching factor. The different types of reactions can be explained easily by a simple scheme that describes the low temperature oxidation of methane: Chain initiating: CH4 + O2 Chain propagating: ˙ 3 + O2 CH CH3 O˙ 2 CH3 O˙ 2 + CH4 ˙ + CH4 OH ˙ + CH2 O OH ˙ + O2 H CO H O˙ 2 + CH4 H O˙ 2 + CH2 O

A

A A A A A A A A

˙ 3 + H O˙ 2 CH

(2.9)

CH3 O˙ 2

(2.10)

˙ CH2 O + OH

(2.11)

˙ 3 CH3 OOH + CH ˙ 3 H2 O + CH ˙ H2 O + H CO

(2.12)

CO + H O˙ 2 ˙ 3 H2 O2 + CH

(2.15)

H2 O2 + H C˙ O

(2.17)

(2.13) (2.14) (2.16)


Chain branching: CH3 OOH CH2 O + O2

A A

Chain terminating: ˙ OH H O˙ 2 ˙ 3 + CH ˙ 3 CH

˙ CH3 O˙ + OH ˙ ˙ H O2 + H CO

A A A

23

(2.18) (2.19)

wall

(2.20)

wall

(2.21)

C2 H6

(2.22)

Reaction 2.9 is the initiation reaction in which the first radicals are formed. This reaction is slow because of the high bond energy of the first C-H bond of CH4 which is 440 kJ/mol (McMillan and Golden, 1982). Reactions 2.10 to 2.17 are propagating reactions, because as many radicals are formed as consumed. Reactions 2.10, 2.12, 2.13, 2.14, 2.15 and 2.16 are fast because they involve a radical and one of the initial reactants. The most important reactions are the branching steps, reaction 2.18 and 2.19, in which two radicals are generated and no radicals are consumed. These steps are necessary in order to obtain a positive net branching factor. The last class of reactions are the termination reactions, in which more radicals are consumed than generated (reaction 2.20 to reaction 2.22). This reaction mechanism is useful for qualitative explanations of the auto-ignition behaviour but cannot predict the auto-ignition limits quantitatively. Therefore more extensive reaction mechanisms are needed which are validated with experimental studies.

2.3.2

Semenov theory of thermal ignition

The Semenov theory of thermal ignition (Semenov, 1935) considers a zerodimensional model of a closed vessel. The temperature of the gas mixture is assumed to be uniform across the whole volume of the system. The wall of the vessel is at a constant temperature and is equal to the initial temperature of the gas mixture. The vessel has a volume V and an inside surface S. The amount of heat release because of the chemical reaction per unit time, q˙r , is given by: by Arrhenius as: qr = V Qcn A exp(−EA /RT ) = V Qρn εn A exp(−EA /RT )

(2.23)

in which Q is the heat of reaction, c is the overall concentration, n is the overall reaction order, A is the Arrhenius pre-exponential factor, EA is the activation energy, R is the molar gas constant, T is the temperature. The concentration c is written as the product of the density ρ and the mass fraction ε of the reacting species. The heat loss to the vessel wall is assumed to be convective, i.e. proportional to the gas-wall temperature difference: qloss = h · S · (T − Tw )

(2.24)

24


Heat Flux

C

B A

qloss Tignit oi n

qr Tcrit ci al

Tstable T0

Temperature

Figure 2.5: The thermal fluxes against temperature according to the Semenov model.

with h the convective heat transfer coefficient, S the internal surface area, and T and Tw the temperature of the gas and of the wall, respectively. The heat production and the heat loss are graphically represented in figure 2.5. Three cases can be distinguished. The heat production can be less than the heat loss, or it can be the same as the heat loss or the heat production is greater than the heat loss. Since the heat production is dependent on the pressure through the density term, three different curves A, B and C are shown in figure 2.5 which represent the heat production curves for increasing initial pressure. The straight line on figure 2.5 is the heat loss qloss . In case the heat production is represented by curve A and if the temperature of the gas mixture is below the temperature Tstable , the temperature will increase till the temperature Tstable is reached. If the temperature is somewhat higher than Tstable the temperature will decrease and will remain constant around the stable temperature. In case the heat production is represented by curve C, the heat production is always higher than the heat loss. The system will self-heat to explosion. The critical condition for auto-ignition exists when the heat production is represented by curve B of figure 2.5. The heat loss curve is tangential to the heat production curve at the critical temperature Tcritical . When the gas mixture is initially at a temperature T0 , the temperature will slowly increase up to the unstable critical temperature. A small perturbation of the temperature will lead to the auto-ignition of the gas mixture. In order to determine the auto-ignition temperature T0 two conditions must be fulfilled


at point Tcritical or Tc :

or

25

qr = qloss dqloss dqr = dT dT

(2.25)

V Qρn εn A exp(−EA /RTc ) = h · S · (Tc − T0 )

(2.27)

(EA /RTc2 )V

(2.28)

n n

Qρ ε A exp(−EA /RTc ) = h · S

(2.26)

At the critical temperature it can be deduced from equations 2.27 and 2.28 that: RTc2 (2.29) (Tc − T0 ) = EA This equation can be arranged into a quadratic form: Tc2 −

EA Tc EA T0 + =0 R R

(2.30)

the solutions of which are: r

2 EA EA T0 −4 ) (2.31) R2 R or r EA RT0 EA ± 1−4 (2.32) Tc = 2R 2R EA The solution with the positive sign is not likely to occur because it results in a very high critical temperature, which is not physically possible. The second root with the negative sign does provide a solution for the critical temperature. This solution can be rewritten as: EA RT0 EA RT0 2 − [1 − (2 Tc = ) − 2( ) − ...] (2.33) 2R 2R EA EA

1 EA ± Tc = ( 2 R

In general (RT0 /EA ) is a small number. The high order terms can thus be neglected to give the approximate equation for Tc : Tc ≈ T0 +

RT02 EA

(2.34)

The reaction rate ω˙ at temperature Tc can be rewritten: ω(T ˙ c)

ρn εn A exp(−EA /RTc ) −EA ≈ ρn εn A exp( ) R[T0 + (RT02 /EA )] −EA = ρn εn A exp( ) RT0 [1 + (RT0 /EA )] −EA ≈ ρn εn A exp( [1 − RT0 /EA )]) RT0 = ρn εn A exp[(−EA /RT0 ) + 1] =

= ρn εn A[exp(−EA /RT0 ]e =

[ω(T ˙ 0 )]e

(2.35)

26


Consequently, the reaction rate at the critical temperature is equal to the reaction rate at the initial temperature times e. The Semenov parameter Ψ represents the ratio between the heat production potential of the reaction and the heat loss potential through cooling: Ψ≡

V Qρn εn A · exp(−EA /RT0 ) hS · RT02

(2.36)

After combining equation 2.28 and equation 2.35 with previous equation, it can be shown that at criticality the Semenov parameter Ψ = 1/e = 0.368. In order to find the pressure dependency of the auto-ignition temperature according to the Semenov model, equation 2.35 and equation 2.29 can be substituted into equation 2.27. This results in: eV Qρn εn A exp(−EA /RT0 ) = hSRT02 /EA

(2.37)

The pressure at the critical temperature is given by the ideal gas law: Pc =

ρRTc M

(2.38)

where Pc is the total pressure at the critical point and M is the molar weight. Combining equation 2.37 and equation 2.38 results in: (

EA Pcn hSRn+1 × exp( ) ) = n+2 nM nE e V QAε RT T0 A 0

(2.39)

hSRn+1 Pcn EA + ln( ) ) = RT0 V QAεn M n EA e T0n+2

(2.40)

or ln(

The order of most hydrocarbon reactions can be estimated to be 2 (Glassman, 1996). Therefore equation 2.40 reduces to the following form: s Pc EA hSRn+1 ln( 2 ) = ) (2.41) + ln( T0 2RT0 V QAεn M n EA e or ln(

Pc EA )= +C T02 2RT0

(2.42)

Equation 2.42 describes the pressure and temperature conditions for thermal auto-ignition. The auto-ignition limit can be represented as a straight line on a logarithmic plot as can be seen in figure 2.6. For a limited temperature range this equation is often reduced to: ln(

EA Pc )= + C0 T0 2RT0

(2.43)

27


auto-ignition area

slope = EA/2R

ln(Pc / T02)

Pressure

auto-ignition area

no auto-ignition ln( hSR 3 / VQA e 2 M2E A e )

no auto-ignition 1/T0

Temperature

Figure 2.6: The critical pressure of the vessel versus the temperature of the wall according to the Semenov model.

2.3.3

Frank-Kamenetskii theory

The thermal ignition theory of Semenov is based on a zero-dimensional model and does not allow for any temperature gradients inside the reacting system. This theory is useable as long as the temperature gradients inside the vessel are small in comparison with the gradient at the wall. Frank-Kamenetskii (1955) was the first to take a thermal gradient in space into account. This is important for reacting mixtures with a low thermal conductivity in parallel with a high heat transfer at the wall. The heat conduction equation for the vessel states that the increase or decrease in temperature is because of the thermal diffusion on the one hand and the heat generation by chemical reactions on the other hand: dT cv ρ = ∇(λ∇T ) + q 0 (2.44) dt where cv is the specific heat at constant volume, λ is the thermal conductivity and q 0 is the volumetric heat release rate. q 0 can be expressed as: q 0 = Q · RR = QZe−E/RT

(2.45)

where Q is the volumetric heat of reaction from the mixture, RR is the reaction rate and Z is a constant containing the normal Arrhenius pre-exponential factor and a concentration term. The boundary condition at the wall of the vessel is: −λ

dT = h · (TL − Tw ) dx x=L

(2.46)

were TL is the temperature of the gas mixture at the wall of the system and the other values have the same meaning as in equation 2.27 of the Semenov theory. The Biot number Bi is a dimensionless number which relates the heat transfer resistance inside a body with that at the surface of the body and is

28


defined as:

hL (2.47) λ The Biot number is a measure for the temperature gradient at the wall of the vessel. A high Biot number results in a temperature TL that is approximately the same as the wall temperature, while a low Biot number results in a TL that is not close to the wall temperature. For a typical reference case used in this work, i.e. a gas mixture of 60 mol% methane in air at a pressure of 5 bar and a temperature of 673 K, the Biot number equals about 10. This means that the temperature gradient in the mixture is higher than the temperature gradient at the wall. This also implies that a zero-dimensional model will result in a poor description of the real situation, since this model does not allow gradients inside the mixture. A one or two-dimensional model will result in a more accurate description of the auto-ignition process of gas mixtures. As a consequence of the high Biot number, the temperature boundary condition can be reduced to: Bi ≡

Tx=L = Tw

(2.48)

A second boundary condition states that there is no temperature gradient at the centre of the vessel: dT =0 (2.49) dx x=0 The temperature of the gas mixture is initially equal to the surrounding wall temperature Tw : T (x) = Tw at t = 0 and 0 ≤ x ≤ L

(2.50)

The solution of equations 2.45 to 2.50 results in a radial temperature distribution as a function of time. The mathematical solution of these equations will not be repeated here, but can be found in Glassman (1996). In this work, see section 5.1, computational methods will be used for solving these equations. However it is interesting to consider the solutions of the Frank-Kamenetskii model to gain insight into the combustion process. These two solution methods are known as the stationary and the non-stationary method. At ignition there is a large temperature gradient. The initially small temperature rise suddenly changes into a steep temperature rise. Therefore no stationary solution of the energy equation exists. As a consequence the critical condition for autoignition is when the energy equation 2.44 has a stationary solution. By further derivations (Glassman, 1996) this condition can be described in terms of the dimensionless Frank-Kamenetskii parameter δ: δ=

Q EA 2 −E A L Ze RTw ≤ δcrit λ RTw2

(2.51)

The Frank-Kamenetskii parameter δ is directly proportional to the reactivity and the pressure by means of Z, the dimensions of the system by L2 and also includes the effect of the ambient temperature through Tw . For a spherical


29

vessel δcrit = 3.32, for an infinite cylindrical vessel δcrit = 2.00 and for infinite parallel plates δcrit = 0.88. The second approximation of the Frank-Kamenetskii theory for thermal ignition is the non-stationary solution. This approximation is the same as that posed by Semenov (1935) since no spatial variation is taken into account. This method can be applied if the major temperature gradient is localised at the wall. However, the Biot numbers for the studied gas mixtures are high and the radial temperature gradient is important. Consequently, this non-stationary solution method has less relevance for this study and will not be treated here, but can be found in Glassman (1996).

30


Chapter 3

Experimental set-up and procedures A theory is something nobody believes, except the person who made it. An experiment is something everybody believes, except the person who made it. Albert Einstein, German born American Physicist (1879 – 1955)

3.1

Experimental set-up

T he auto-ignition experiments were conducted in the Laboratory for Industrial Safety. The laboratory contains four explosion bunkers in which it is possible to perform safely experiments at high pressures and temperatures. This paragraph will describe the experimental set-up in more detail. The experimental set-up, illustrated by figure 3.1, consists of four major parts: the mixture preparation equipment, the buffer vessel, the explosion vessel and the data acquisition system.

3.1.1

Mixture preparation equipment

The mixture preparation equipment consists of three mass flow controllers (MFC’s), a liquid pump, a mixing vessel and an evaporator. The different components of the gas mixture (e.g. air, methane, propane and butane) are supplied in high pressure cylinders. The air and methane cylinders have a filling pressure of 200 bar and therefore, they can be expanded directly throughout the mixture preparation equipment to perform experiments with an initial pressure up to 100 bar. For the condensed fuels the pressure inside the cylinder is equal to their saturation pressure. At room temperature this pressure is equal to 7.3 bar and 1.8 bar for propane and n-butane respectively. Because of this low sat-

31

Chapter 3 Experimental set-up and procedures

Figure 3.1: Experimental set-up.

32

3.1 Experimental set-up

33

! " !

# $

Figure 3.2: Calibration curve of Mass Flow Controller (MFC A) for methane.

uration pressure the pressure of the fuel needs to be raised by means of a liquid pump. To produce homogeneous mixtures of a desired composition, the fuel and the air are supplied to the buffer vessel using the constant flow method, i.e. the different components of the mixture flow simultaneously through the mixing vessel to the buffer vessel. The composition is determined based upon the mass flow rates of the different components. Gas chromatography was used at regular intervals to verify the mixture composition and the accuracy is found to be 0.5 mol%. MFC’s The three mass flow controllers A, B and C (Bronkhorst Hi-Tec) have different nominal flow rates, namely 50, 20, and 4 Nl/min 1 for air. In case other gases than air are used, conversion factors supplied by Bronkhorst can be used to estimate the nominal flow rate. In order to increase the accuracy of the mixing method the MFC’s were calibrated by means of a volumetric drumtype gas meter (Ritter). The calibration curve with the standard deviations of MFC A for methane is shown in figure 3.2. A five point calibration has been performed. The calibration of the mass flow controller shows excellent linearity over the total setting range. The nominal flow rate for methane is 38.2 Nl/min instead of 50 Nl/min for air. The mass flow control panel is shown in figure 3.3. The pressure of each mass flow controller is adjusted by means of a pressure reducer before the MFC and a back pressure regulator after each MFC. Liquid pump A volumetric metering pump was used to supply the liquid fuels. The pump is a combination of a Gilson HPLC driving unit and an Orlita 11

Nl = 1 l at 1 atm and 0 ℃.

34


MF65 membrane pumping head. A picture of the pump installation is shown in figure 3.4. The fuel cylinder is provided with a dip tube. The fuel is held at a pressure of 12 bar under a nitrogen blanket. A water cooling device cools the fuel through a heat exchanger and maintains the pump head at a constant temperature of 10 ◦ C in order to prevent the evaporation of the fuel and to guarantee a constant mass flow. A back pressure regulator situated after the pump ensures that the outlet pressure remains constant at 50 bar. The liquid pump was calibrated with the liquid fuel and equal temperature and pressure settings. The volume rate was measured by means of a pipette. The calibration curve of the pump for propane is shown in figure 3.5. The nominal flow of the liquid pump for water is 10 ml/min. In case liquid propane is used the nominal flow amounts to 7.15 ml/min only. The calibration curve shows an excellent linear correlation. Mixing vessel The gases, e.g. methane and air, coming from the mass flow controllers are mixed homogeneously inside the mixing vessel. Evaporator The evaporator ensures evaporation of the liquid fuel. The liquid fuel drips into the gas flow and is subsequently heated. The evaporator consists of a 3 m copper tube embedded in an electrically heated concrete mass. The evaporator has a design pressure of 300 bar at a maximum temperature of 300 ◦ C. For all experiments with liquid fuels the temperature was set to 120 ◦ C and the pressure was set to at least 10 bar by means of the back pressure regulator that is positioned after the evaporator. It is important that the pressure of the gas mixture is sufficiently below its vapour pressure in order to avoid condensation of the fuel. The vapour pressure is correlated with temperature by numerous methods. The classic simple equation for correlation of low to moderate pressures is the Antoine equation: ln P sat = A +

B T +C

(3.1)

A, B and C are regression constants. At high pressure the Antoine equation does not fit the vapour pressure accurately (Perry and Green, 1999). Therefore, a regression with the modified Riedel equation (Equation 3.2) is used in this work to calculate the vapour pressure of the liquid fuel. ln P sat = A +

B + C ln T + DT E T

(3.2)

A, B, C and D are regression constants and E is an exponent equal to 1 or 2 depending on which regression gives the most accurate fit. These coefficients are summarised in table 3.1 for the liquid fuels applied in this work. The temperature and concentration dependency of the vapour pressure for n-butane/air mixtures is shown in figure 3.6. From this figure, it can be deduced that for a temperature of 120 ◦ C and a pressure of 55 bar the butane concentration is maximum 40 mol% in order to avoid condensation.

35


Figure 3.3: Gas mixing installation.

Back pressure

Pump

Cooling Figure 3.4: Liquid pump installation.

fuel propane n-butane i-butane

A 59.08 66.34 100.18

B -3492.60 -4363.20 -4841.90

C -6.07 -7.05 -13.54

D 1.09e-05 9.45e-06 2.01e-02

E 2 2 1

Table 3.1: Regression coefficients of the modified Riedel equation for propane, nbutane and i-butane.

36


%

!"# $ $ #& !"# $ $

'

Figure 3.5: Calibration curve of liquid pump.

3.1.2

Buffer vessel

The homogeneous gas mixture flows from the evaporator into the buffer vessel. This spherical vessel has a volume of 8 dm3 (internal diameter of 248 mm) and is made of 26 Ni Cr Mo V 14 6 steel. It is designed to withstand explosion pressures up to 3500 bar at a wall temperature of 350 ◦ C. The vessel can be used to determine flammability limits when an ignition source is introduced as is described in more detail by Van den Schoor (2007). In this study the buffer vessel is used to maintain the premixed reactants at high pressure (up to 50 bar) and at a temperature of 120 ◦ C in order to accelerate the filling of the explosion vessel. On the one hand the temperature must be sufficiently high to avoid condensation of the fuel and also pre-oxidation of the gas-mixture must be avoided. Since the temperature of 120 ◦ C is some 200 ◦ C below the auto-ignition temperatures of the different fuels, pre-oxidation does not occur. The vessel is equipped with three electrical heating units to obtain uniform temperature. The piping between the evaporator, the buffer vessel and the explosion vessel is also heated to a temperature of 120 ◦ C by means of electrical rope heaters to avoid condensation of the fuel.

3.1.3

Explosion vessel

The second vessel is the explosion vessel. It has a spherical volume of 8 dm3 and is made of X 2 Cr Ni Mo 18 10 steel. The vessel is equipped with three electrical heating units to obtain a uniform temperature. It is designed to withstand pressures up to 250 bar at temperatures up to 550 ◦ C. The vessel

37


Saturation pressure [bar]

200

20 mol% 40 mol% 60 mol% 80 mol% 100 mol%

150

100

50

0 0

20

40

60

80

100

120

140

160

180

200

Temperature [°C]

Figure 3.6: Vapour pressure curve of n-butane/air mixtures as a function of the n-butane concentration.

has one large opening at the top through which it is possible to clean the vessel. It also has several small gaps for the temperature and pressure measurements and if necessary for an ignition source. A picture of the buffer vessel and of the explosion vessel inside the explosion bunker is presented in figure 3.7.

3.1.4

Data acquisition

The data acquisition system consists of a pressure and temperature measuring system. The data are collected by a data scanner (Labview 6.1 of National Instruments). The scan frequency is 1000 Hz, which is sufficient to follow the pressure and temperature rises during the auto-ignition. The following paragraphs will discuss in detail the different measuring systems. Pressure measuring system The pressures in both vessels are measured with Baldwin 5000 psi strain gauges. These static pressure transducers are based on the piezo-resistive effect, in which the resistance of the transducer changes depending on the applied force. To avoid temperature influence on the pressure transducer a connecting pipe, cooled by a water bath at 10 ◦ C, is placed between the explosion vessel and the transducer. The pressure transducers are connected to an amplifier, which transforms the pressure signal to a 0-5 V signal. The maximum pressure of the pressure transducer is 5000 psi or 350 bar. The amplification factor is adjusted that the measured pressure range corresponds to the 0-5 V range. The voltage signal is subsequently read in by the computer by means of a 16 bits PCI-6032E data acquisition card produced

38


Buffer vessel

Explosion vessel

Figure 3.7: Picture of the buffer and the explosion vessel.

by National Instruments. The pressure transducers were calibrated by means of a static pressure system (Scantura B20: multifunction calibrator) and their error is below 1%. Temperature measuring system The thermocouples used in this study are Chromel-Alumel type K thermocouples. Thermocouples differ also in type of construction, as can be seen in figure 3.8. With the ungrounded thermocouple there is no direct contact between the junction and the covering. As a consequence the thermocouple is highly wear-resistant and is also resistant to interference noise. A second type is the grounded thermocouple, in which there is direct contact between the junction and the shield. The third type is the exposed thermocouple. The thermocouple junction here is exposed to the surroundings and is not protected from wear. The advantage of this type of thermocouple is its short response time. The number and type of thermocouples has changed several times during this study. At first the temperature was measured with one ungrounded thermocouple (with an external diameter of 1 mm) at the centre of the vessel. Since the temperature increase is most significant at the top of the vessel because of the buoyancy, a second ungrounded 1 mm thermocouple was added at the top of the vessel. In order to study the buoyancy in detail a set-up was used with three exposed thermocouples with an external diameter of the junction of 500 µm. The thermocouples were located at the centre, 6 cm above the centre and at the top of the vessel. The error on the temperature measurement is described in section 3.3.

3.2

Experimental procedure

The following procedure is applied to determine the auto-ignition limits and the ignition delay times. First the evaporator, the buffer vessel and the explosion vessel are heated to the required temperature and kept at this temperature. Subsequently, the buffer vessel is brought to vacuum pressure and purged with

39

3.2 Experimental procedure

Grounded

Ungrounded

Exposed

Figure 3.8: Different types of thermocouple 3

1100 Top Temp

Maximum Ignition Delay Time 1000

Elevated Temp

Ignition Delay Time

Pressure

2

800 700

1.5

600 1

Pressure [MPa]

Temperature [K]

2.5

Central Temp

900

500 0.5 400 300 0

10

20

30

40

50

60

70

80

90

0 100

Time [s]

Figure 3.9: Recorded pressure and temperature histories in the explosion vessel ("Top Temp" represents the temperature at the top of the vessel while "Elevated Temp" and "Central Temp" respectively represents the temperature 6 cm above and at the centre of the vessel).

a mixture volume of at least ten times the volume of the buffer vessel. Next, the buffer vessel is filled to a pressure of 2 to 5 MPa depending on the initial pressure of the test. The evacuation and the subsequent flushing ensure an accurate and homogeneous fuel mixture in the buffer vessel. Thereafter the explosion vessel is evacuated to a pressure below 1000 Pa. Finally, the explosion vessel is filled to the desired pressure with the premixed gas mixture by opening the pneumatic valves between the buffer and the explosion vessel. This filling procedure guarantees a constant filling time for a specific pressure of the buffer vessel because of the choked gas flow in the connecting tubing. After each experiment the explosion vessel is emptied and flushed with air during 2 minutes to ensure that the amount of residual gases is negligible. Thereafter the buffer vessel is refilled to its initial pressure and a new experiment can be performed. Figure 3.9 shows a typical time history of pressure and temperature inside the explosion vessel during an experiment. The filling time varied from

40


Type of reaction No reaction Auto-ignition

Temp.a and Rel. press. rise < 50 K and < 10% > 50 K or > 10%

Ignition delay time > 15 min < 15 min

Table 3.2: Classification criteria for propane and butane. /a The temperature rise is measured with two ungrounded thermocouples with a diameter of 1 mm.

Type of reaction No reaction Slow Combustion Auto-ignition

Temperature rise b < 50 K > 50 K and < 200 K > 200 K

Ignition delay time > 10 min < 10 min < 10 min

Table 3.3: Classification criteria for methane. /b The temperature rise is measured with exposed thermocouples with a diameter of 0.5 mm.

5 to 30 seconds, depending on the pressures of the buffer and explosion vessel. This filling time causes an uncertainty in the ignition delay time (IDT), which is the time lag between the completed injection of the test mixture and any exothermic phenomenon (see figure 3.9). The IDT’s presented in this work do not include the filling time. The occurrence of an auto-ignition is judged from the pressure and temperature histories. The classification criteria are slightly different from propane and butane compared to methane as can be seen in tables 3.2 and 3.3. For propane and butane a combined temperature and pressure criterion is applied. When the temperature rise is smaller than 50 K within 15 minutes after filling the vessel and the pressure increase is smaller than 10%, it is concluded that auto-ignition did not take place. A temperature rise of more than 50 K or a pressure rise of more than 10% within a time period of 15 min is classified as an auto-ignition. The maximum ignition delay time is chosen to be 15 minutes which is of the same order of magnitude as those used in other studies or standards (Safekinex (2005), Kong et al. (1995), EN 14522 (2005)). In order to compare the auto-ignition limits of the methane/air mixtures to those obtained by Caron et al. (1999), their ignition criterion is adopted. This criterion is a single temperature rise criterion. When the temperature rise is smaller than 50 K within 10 minutes it is concluded that auto-ignition did not take place. A maximum temperature rise above 200 K is classified by these authors as an auto-ignition, while a temperature rise between 50 K and 200 K is classified as a slow combustion. Because of the thermal inertia of the explosion vessel, it is not feasible to change the explosion vessel temperature between two experiments in order to find the auto-ignition temperature. Instead of varying the temperature, the initial pressure was varied at a constant vessel temperature. An example of the auto-ignition data of a 50 mol% n-butane/air mixture is presented in figure 3.10.

3.3 Analysis of the temperature measurement error

41

2.5

Auto-ignition No reaction AIT limit

Initial pressure [MPa]

2

1.5

1

0.5

0 490

500

510

520

530

540

550

Initial temperature [K]

Figure 3.10: Determination of the auto-ignition limit of a 50 mol% n-butane/air mixture.

3.3

Analysis of the temperature measurement error

In order to measure the gas temperature inside the explosion vessel, one or more type K thermocouples are inserted inside the explosion vessel. The type K thermocouple is commonly used and consists of a positive Ni-Cr wire in combination with a negative Ni-Al wire and has a temperature range from -270 ◦ C up to 1372 ◦ C. The sensitivity of this thermocouple amounts to 40 µV /◦ C. The measurement errors have to be analysed. The error on gas temperature measurement can be subdivided into three categories: • First there is the error on the probe temperature measurement. The reading of the data acquisition system is not the actual probe temperature. The manufacturer of the thermocouples, OMEGA, prescribes a relative error of 0.5% for the type K thermocouples. • The next group of errors originates from the temperature difference between the gas temperature and the probe junction temperature. These errors can be explained by the steady state energy equation: qc + qr + qd = 0

(3.3)

where qc represents the convective heat flux from the boundary layer to the probe junction, qr represents the heat transfer from the probe by radiation and qd the heat transfer by conduction. For type K thermocouples the catalytic reactions between the metals and the surrounding gases are generally negligible. Consequently there is no heat source term resulting from catalytic reactions in the energy equation. The respective errors are

42


the conduction error EC and the radiation error ER . The conduction error is described by Arts et al. (2001): EC = TG − TJ =

TG − TM 4h 1/2 cosh(L( Dλ ) )

(3.4)

where TG is the gas temperature, TJ is the junction temperature, TM is the temperature of the probe stem, L is the length for conduction, h is the convective heat transfer coefficient, D is the diameter of the wire comprising the thermocouple and λ is the thermal conductivity of the thermocouple material. The radiation error ER is calculated by considering the energy equation and neglecting the heat transfer by conduction. The heat transfer by radiation has two parts. Firstly there is the thermal radiation from the probe to the cold wall of the vessel and secondly there is the thermal radiation from the hot burning gas to the probe: FJ→W τ 0 σSR J (TJ4 − Tw4 ) − FJ→G σSR J (TG4 − TJ4 ) = hSc (TG − TJ ) (3.5) where F is the view factor, τ 0 is the transmittance through the gas mixture, σ is the Stefan Boltzmann constant (5.67 10−8 W/m2 K 4 ), SR is the radiation heat transfer area, J is the emissivity of the probe, TW is the temperature of the surrounding walls and Sc is the area for heat transfer by convection. The radiation error can be obtained from equation 3.5 by omitting the surface areas and the view factors: ER = TG − TJ =

τ 0 σJ (TJ4 − Tw4 ) − σJ (TG4 − Tw4 ) h

(3.6)

This equation has to be solved iteratively since the temperature of the gas is on both sides of the equality sign. Notice that this result is independent of the emissivity of the surrounding wall. After analysing the above equations it becomes clear that the heat transfer coefficient is to be maximised in order to reduce the conduction and radiation error. It is difficult to determine the heat transfer coefficient when an auto-ignition occurs inside a closed vessel. The heat transfer coefficient during the auto-ignition can be calculated for a forced convective flow along the thermocouple. The natural convective flow is in fact a forced flow from the point of view of the thermocouple. The heat transfer coefficient is determined using a correlation for the Nusselt number valid for forced convective flow along cylinders which are normal to the flow direction: N u = (0.44 ± 0.06)(Re)0.50

(3.7)

With N u = hcλD and Re = v·D ν , where λ is the thermal conductivity of the gas, D is the junction diameter, v is the flow velocity and ν is the kinematic viscosity of the gas. • Finally the temperature of the junction is not immediately equal to the gas temperature. The response of a thermocouple may be modelled as a


43

first order system. When a thermocouple is subjected to a rapid temperature increase, it will take some time to respond depending on the time constant of the thermocouple. The transient error is given by: ET = TG − TJ = τ with τ=

dTJ dt

mCp ρCp D = hSc 6h

(3.8)

(3.9)

where τ is the thermocouple time constant, m is the mass of the thermocouple junction, Cp is the specific heat of the thermocouple material, Sc is the area for heat transfer by convection and ρ is the density of the thermocouple material. Figure 3.11 shows the responses of three thermocouples with different time constants to a sudden temperature increase of 200 K with a duration of 3 seconds. It can be seen from figure 3.11 that only the thermocouple with a time constant of 0.5 s is able to measure the steep temperature increase. The exposed thermocouple used in this study with a junction diameter of 500 µm has a time constant of 1.3 s, while the ungrounded 1mm thermocouple has a time constant of 4s according to Omega, the manufacturer of the thermocouples. This means that the exposed thermocouple responds 3 times faster than the ungrounded 1mm thermocouple. This ratio is also retrieved from the theoretical analysis. The exposed thermocouple with a time constant of 1.3 s has a maximum temperature increase of 180 K, while the ungrounded thermocouple only shows a temperature increase of 100 K in comparison with the applied temperature increase of 200 K. As an example, these errors on the temperature measurement are calculated for an auto-ignition experiment with a 60 mol% methane/air mixture at an initial temperature of 683 K and an initial pressure of 1.7 MPa when a temperature increase of 200 K is measured with an exposed thermocouple with a diameter of 0.5 mm. The buoyancy driven flows have a velocity magnitude of 2 ± 1 cm/s along the vertical axis of the sphere. This is retrieved from the CFD calculations of this study, see section 5.2. For the calculation of the radiation error, the transmittance τ 0 through the gas mixture has to be calculated. The transmittance is the fraction of the incident energy that passes through the gas volume. This is equal to the incident energy minus the energy absorbed by the gas when the reflection or the scattering is neglected. Kirchhoff’s law states that the absorbance α is equal to the emittance : τ0 = 1 − α = 1 −

(3.10)

According to Hubbard and Tien (1978) the emittance can be described in function of the Planck mean absorption coefficient κM and the path length L, which is equal to the radius R of the vessel: = 1 − e(−κM L)

(3.11)

44


Temperature increase [K]

250

time constant = 0.5s time constant = 1.3s time constant = 4s

200

150

100

50

0 0

1

2

3

4

5

6

7

8

9

10

11

Time [s] Figure 3.11: Response of a thermocouple to a temperature increase step of 200K.

The Planck mean absorption coefficient κM is calculated from the Planck mean absorption coefficients κp,i of the different radiating species, such as CH4 , CO2 , CO and H2 O, via: X κM = pi κp,i (T ) (3.12) i

with pi the partial pressure of the radiating species and κp,i (T ) are obtained from Hubbard and Tien (1978). The Planck mean absorption coefficient is directly proportional to the absolute pressure of the gas mixture. Consequently, the radiation error is depending on the pressure of the gas mixture. Since the path length influences the absorption of the gas layer, the radiation error will be different for the three thermocouples, positioned at the centre, 6 cm above the centre and at 1 cm from the top of the vessel. For the thermocouple positioned at the top of the vessel the path length to the top side of the vessel is much smaller than for the elevated temperature and for the central thermocouple. Table 3.4 gives an overview of the error on the probe temperature and the errors by conduction and radiation for a temperature increase of 200 K. It can be seen that the radiation losses in particular for the thermocouple positioned at the top of the vessel give rise to a significant error on the temperature measurement. Table 3.5 presents the influence of the pressure on the radiation error. At a pressure of 1 bar or 0.1 MPa the radiation error is larger than at a pressure of 1.7 MPa due to the lower absorption capacity of the gas mixture and consequently the higher radiation heat loss from the probe junction to the


Error type probe temperature error conduction error radiation error (top therm.) radiation error (elevated therm.) radiation error (central therm.)

45

Value 3K 1K 17 K 2K 0.06 K

Table 3.4: The absolute errors on the temperature measurement evaluated for a temperature increase of 200 K measured with exposed 0.5 mm thermocouples.

Error type radiation error (top therm.) radiation error (elevated therm.) radiation error (central therm.)

Value for 0.1 MPa 45 K 41 K 40 K

Value for 1.7 MPa 17 K 2K 0.06 K

Table 3.5: The influence of pressure on the radiation error evaluated for a temperature increase of 200 K measured with exposed 0.5 mm thermocouples.

wall. The effect of the position of the thermocouple increases with increasing pressure. At a pressure of 0.1 MPa the radiation error has only a temperature difference of 5 K for the different thermocouples, while at a pressure of 1.7 MPa the radiation error differs 17 K between the central thermocouple and the thermocouple at the top of the vessel. The last type of error is the transient error. Figure 3.12 presents the temperature history of an auto-ignition with a 60 mol% methane/air mixture at a temperature of 683 K and a pressure of 1.7 MPa measured with three exposed thermocouples. Figure 3.13 represents the temperature history if the thermocouples would have a time constant of 4s instead of 1.3 s. After comparison of both figures, it can be seen that the ungrounded thermocouples would not be able to follow the steep temperature increase and the central thermocouple would only measure a temperature increase of 122 K instead of a temperature increase of 202 K. Figure 3.14 presents the calculated temperature histories in case three fast thermocouples with a time constant of 0.5 s would have been used. It can be seen that the maximum temperature would slightly increase (20 K) for the thermocouple at the top of the vessel while the maximum temperature of the central thermocouple would measure the same maximum temperature as the other thermocouples. It can be concluded that the transient error and the radiation error give rise to the largest errors on the temperature measurement. Therefore attention must be paid if the auto-ignition criterion is based on a temperature measurement. As can be seen from this analysis, one ungrounded central thermocouple with a large time constant is incapable of capturing the maximum temperature rise. A combined temperature and pressure criterion is advised in order to assess the auto-ignition.

46


700

Original temperature history Time constant = 1.3 s

Top Temp 650

Elevated Temp

Temperature [°C]

Central Temp 600

550

500

450

400 300

310

320

330

340

350

360

370

380

390

400

Time [s]

Figure 3.12: Temperature history of an auto-ignition measured with three exposed thermocouples with a time constant of 1.3 s.

700

Time Constant = 4 s Top Temp 650

Elevated Temp

Temperature [°C]

Central Temp 600

550

500

450

400 300

310

320

330

340

350

360

370

380

390

400

Time [s]

Figure 3.13: Calculated temperature history of an auto-ignition measured with three exposed thermocouples with a time constant of 4 s.

47

3.4 Fuel Type

700

Time Constant = 0.5 s Top Temp

650

Elevated Temp

Temperature [°C]

Central Temp 600

550

500

450

400 300

310

320

330

340

350

360

370

380

390

400

Time [s]

Figure 3.14: Calculated temperature history of an auto-ignition measured with three exposed thermocouples with a time constant of 0.5 s.

3.4

Fuel Type

The combustible gases that will be studied are methane (CH4 ), propane (C3 H8 ), n-butane (C4 H10 ) and i-butane (C4 H10 ). Methane is the simplest alkane. It is the principal component of natural gas. It is commonly used as a fuel in thermal power stations or in households because it has a clean burning process with low CO2 emissions compared to higher alkanes and coal. Methane is also commonly used in the chemical industry as a feedstock for the production of for example, hydrogen, methanol, acetic acid and acetic anhydride. In this thesis the experiments are performed with pure methane and not with natural gas in order to avoid the influence of other unknown components on the auto-ignition limits. The methane gases are supplied in high pressure cylinders (200 bar) with a purity of 99.95%. The other fuels studied in this thesis are the higher alkanes with three or four carbon atoms. These can be classified under the name LPG (Liquefied Petroleum Gas) which is commonly used for a mixture of propane, i-butane and n-butane. LPG has many applications. For example, it can be a base material for many chemical processes, it is a well-known motor fuel. Propane is used as propellant in aerosols in substitution for the noxious chlorofluorocarbon gases and propane can also serve as a cooling agent in refrigerating machines. Just as any other gas it consists of small traces of other fuel products. The maximum quantity of these impurities is determined by the standard NBN T 52-706 (2000). The composition of LPG is not fixed, but depends on the country and may also change with the season. This variation in composition

48


Component propane i–butane n–butane

Boiling temperature [◦ C] -42.1 -11.7 -0.5

Vapour pressure at 21◦ C [MPa] 0.86 0.31 0.21

Table 3.6: The boiling temperature and the vapour pressure of the components of LPG.

is due to the different boiling-points of the different components. Table 3.6 presents the respective boiling temperatures at atmospheric pressure and the vapour pressures at a temperature of 21◦ C. Propane is the most volatile component of LPG. Increasing the concentration of propane in the LPG mixture will lower the boiling temperature of the LPG mixture. A high volatility is necessary when the outside temperature is low. On the other hand in warm regions a high concentration of butane is advised. In Belgium during winter the propane/butane ratio is 70/30, while during summer the propane/butane ratio is 60/40. In France the propane/butane ratio is about 35/65, while in Spain the LPG mixture consists mostly of butanes. In this study at first the pure components of LPG were tested. These fuels were supplied in pressure cylinders with a purity of 99.9%. Instead of using commercial LPG mixtures with traces of impurities to determine the autoignition behaviour, it is chosen to work with two pure mixtures of propane, i-butane and n-butane. The first LPG mixture studied has a composition of 50 mol% propane and 50 mol% n-butane. The second mixture has the following composition: 40 mol% propane, 30 mol% iso-butane and 30 mol% n–butane. The maximum error on the concentrations of the different components is 1.5 mol%.

Chapter 4

Experimental results: The men of experiment are like the ant; they only collect and use. But the bee . . . gathers its materials from the flowers of the garden and of the field, but transforms and digests it by a power of its own. Leonardo Da Vinci, Italian draftsman (1452 – 1519)

T he main objective of the experimental part of this study is to obtain a large set of auto-ignition temperatures at elevated pressures for different gas

mixtures. On the one hand these data can be used directly to assess the autoignition risk of industrial installations and on the other hand these data will be used for the validation of the simulation models. The experimental part of this study consists of the determination of the auto-ignition temperatures of the lower alkane/air mixtures, in particular methane, propane, n-butane and i-butane in air at pressures up to 3 MPa. This part consists first of experiments with propane/air and butane/air mixtures (Section 4.2 and Section 4.3). These are the main components of liquified petroleum gas (LPG). At first the auto-ignition limits are determined for each individual fuel component in air. Thereafter two different LPG mixtures are tested in order to compare the influence of the different components on the auto-ignition temperature of a mixture. The experiments with methane/air mixtures (Section 4.5) are an addition on the data obtained by Caron et al. (1999). Since the numerical study mainly focuses on the auto-ignition limits of methane/air mixtures, it was necessary to gain more insight into the experimental phenomena in order to compare the numerical results with the experimental data of methane/air mixtures. Knowledge of the auto-ignition domain is also relevant for the determination of flammability limits at elevated pressure and temperature. In section 4.4 the experimental upper flammability limits of propane and n-butane are compared with their respective auto-ignition areas in order to clarify some observations. In section 4.1 the auto-ignition limits at atmospheric pressure of the different fuels used in this study are presented.

49

50

Chapter 4 Experimental results:

Temperature [K] 733 713 703 693 693 688 688 683 678 678 678 678 673 673 668

Quantity 60 ml 40 ml 20 ml 40 ml 20 ml 20 ml 60 ml 60 ml 60 ml 40 ml 20 ml 80 ml 60 ml 30 ml 60 ml

Flammable (+/-) + + + + + + + -

Table 4.1: Determination of the auto-ignition temperature of n-butane according to the European standard EN 14522 (2005).

An overview of the experimental data can be found in Appendix A. Part of the experimental results of propane/air mixtures have been published in an international journal with review (Norman et al., 2006).

4.1

Auto-ignition limits at atmospheric pressure

First the auto-ignition temperatures are determined at atmospheric pressure according to the EN 14522 (2005). The standard is described in section 2.2.1. Table 4.1 presents the test series for the determination of the auto-ignition temperature of n-butane. From table 4.1 it can be deduced that the autoignition temperature of n-butane according the EN 14522 is 683 K or 410 ◦ C ± 5 K. Table 4.2 gives a comparison of the auto-ignition temperatures obtained in this study according to the EN 14522 with the auto-ignition data recommended by the Chemsafe (2006) database. It can be seen that the measured auto-ignition temperatures are generally 20K higher than the respective temperatures from the Chemsafe database. This difference corresponds to the average deviation in experimentally determined AIT-values in literature, which is about 30K (Tetteh, J. et al., 1996). The auto-ignition temperature decreases significantly with increasing chain length and the branched i–butane has a higher auto-ignition temperature in comparison with n–butane. The autoignition temperatures of the propane/butane mixtures is situated somewhere between the auto-ignition temperatures of their respective components. The auto-ignition temperature of different alkane/air mixtures can be predicted by the rule of thumb of Ryng (1985), which is described in section 2.1.2. Table 4.3

4.2 Auto-ignition limits of propane/air mixtures

Fuel

measured AIT [EN 14522 (2005)]

methane propane i–butane n–butane 50/50 n-butane/propane 40/30/30 propane/i–/n–butane

893 763 753 683 743 733

K K K K K K

51

AIT [Chemsafe (2006)] [DIN 51794 (1969)] 868 K 743 K 733 K 638 K – –

Table 4.2: Comparison of the measured auto-ignition temperatures (AIT) determined in this study with the AIT from the Chemsafe (2006).

Fuel 50/50 n-butane/propane 40/30/30 propane/iso- and n-butane

measured AIT 743 K 733 K

AIT [Ryng] 723 K 736 K

Table 4.3: Comparison of the measured auto-ignition temperatures (AIT) of propane/butane mixtures with the predicted auto-ignition temperatures determined by a correlation of Ryng (1985).

compares the measured data with the predicted ones. The predicted and the measured auto-ignition temperature of the 50/50 mol% n-butane/propane mixture differ by 20 K, while for the 40/30/30 mol% propane/i–butane/n–butane mixture the measured AIT corresponds very well with the predicted value.

4.2

Auto-ignition limits of propane/air mixtures

This section and the following sections (Section 4.3 and 4.5) present the experimental auto-ignition limits at elevated pressures determined according the new standard operating procedure, which is developed in this study (see Section 3.2). This section present the results of the propane/air mixtures. First the auto-ignition limit is determined for a mixture with a concentration of 40 mol% propane in air. The propane concentration in air can also be expressed in terms of the excess air factor λair or the equivalence ratio φ: λair =

1 [Xair /Xf uel ]mixture = φ [Xair /Xf uel ]stoichiometric

(4.1)

where X stands for the molar fraction. Since the stoichiometric concentration of propane in air is equal to 4.03 mol%, a 40 mol% propane/air mixture corresponds with an equivalence ratio φ of 16 or an excess air factor λ of 0.063. The mixtures that are tested in this study vary from rich to highly rich mixtures, because these mixtures have the lowest auto-ignition temperatures at elevated pressures. This is also observed by Kong et al. (1995) for propane/air mixtures.

52


1.8

Autoignition No reaction

Initial Pressure [MPa]

1.6 1.4 1.2 1

ignition

0.8 0.6 0.4

no ignition

0.2 0 520

530

540

550

560

570

580

Temperature [K]

Figure 4.1: The auto-ignition limit of propane-air mixtures as a function of the initial temperature, determined for 40 mol% propane in air.

A few tests with lower concentrations are performed with the different mixtures to confirm the increase of the auto-ignition limit at low concentrations. Because of the thermal inertia of the explosion vessel, the auto-ignition limit is determined at a constant vessel temperature and a varying pressure. The auto-ignition limit is determined with a step-size of maximum 0.05 MPa. The auto-ignition criterion is a combined temperature and pressure rise criterion. When a temperature rise of minimum 50 K or a pressure rise of more than 10 percent of the initial pressure is measured within a time span of fifteen minutes, it is concluded that auto-ignition occurred. In the first two series one ungrounded 1 mm thermocouple is positioned at mid-height near the wall of the vessel. In the third series of experiments two ungrounded 1 mm thermocouples are used. One is positioned at mid-height near the wall and the other at the top of the vessel. As can be seen from the error analysis of the temperature measurement in section 3.3, these thermocouples have a large time constant and cause significant transient errors. Therefore attention must be paid when a temperature criterion is applied. From the experiments it is observed that the maximum ignition delay time of fifteen minutes is the determining criterion at low concentrations and at low temperatures. For increasing initial temperatures and concentrations the criterion that determines the auto-ignition shifts to the pressure rise criterion. The temperature rise is never the determining criterion but can be used in order to assess the auto-ignition or to compare with the numerical simulations made of this study. The result of one test series with a 40 mol% propane/air mixture is summarised in figure 4.1. The pressure limit for auto-ignition increases with decreasing initial temperatures. At atmospheric pressure the auto-ignition temperature is equal to 573 K, while at an initial pressure of 1.45 MPa the autoignition temperature decreases to 523 K. An exponential correlation can be

53

4.2 Auto-ignition limits of propane/air mixtures

9

8

ln(p/T0)

7

6

5

4 1.70

1.75

1.80

1.85

1.90

1.95

1/T0 [1e-3/K]

Figure 4.2: Pressure dependency of the AIT for 40 mol% propane in air mixture correlated by a Semenov correlation.

deduced for the temperature influence of the auto-ignition limit. In figure 4.2 the pressure dependency of the auto-ignition temperature is correlated by the Semenov correlation (Section 2.3.2): ln(

Pc B )= +C T0 T0

(4.2)

where Pc is the lowest pressure at which an auto-ignition occurs [Pa], T0 is the auto-ignition temperature [K] and B and C are two fitting constants. This approximation is acceptable for a limited temperature range as can be seen on figure 4.2. Figure 4.3 shows the pressure dependence of the ignition delay times for three different ambient temperatures with a 40 mol% propane in air mixture. An increase of the temperature or the initial pressure causes a decrease of the ignition delay time. The ignition delay time is inversely proportional to the initial pressure. This correlation is also derived by the Frank–Kamenetskii theory (Glassman, 1996). The error margins are not shown on figure 4.1, but can be estimated to be 0.05 MPa for the auto-ignition pressures, since the step-size introduces the largest error in comparison with the temperature and pressure measurement errors. The error on the pressure measurement is estimated to be below 1%, which corresponds to 0.02 MPa for a pressure of 2 MPa, and the error on the temperature measurement is maximum 2 K. A main difficulty in the determination of the auto-ignition limit is the reproducibility of the tests if they are performed at different times. Therefore three series of tests spaced over one year were performed to investigate the reproducibility of the auto-ignition limit. Figure 4.4 presents the auto-ignition

54


1600

523 K 536 K 548 K

1400

Ignition delay time [s]

1200 1000 800 600 400 200 0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8


Figure 4.3: Ignition delay times as function of the initial pressure determined for 40 mol% propane in air.

limits of the three different test series of a 40 mol% propane/air mixture. It can be seen that for high temperatures the reproducibility is quite good while at a temperature of 523 K the reproducibility is poor. Because the auto-ignition pressure increases exponentially at lower temperatures, a significant variation on the auto-ignition pressure reduces to an acceptable variation on the autoignition temperature. Because the propane concentration which is most sensitive to auto-ignition can be dependent on the initial pressure, different concentrations from 10 mol% up to 70 mol% are tested at different auto-ignition pressures. The results are summarised in figure 4.5. The concentration most sensitive to auto-ignition, which is 30 mol% to 40 mol% propane in air at a temperature of 573 K, increases for increasing pressure and decreasing temperature. At a temperature of 523 K the minimum auto-ignition limit lies at a concentration higher than 70 mol% propane. Because of the saturation pressure of propane it is impossible to perform tests at a temperature of 523 K with higher concentrations. The second series only consists of experiments with 40 mol% propane and is therefore not shown on figure 4.5. The third series consists of experiments with 30 to 60 mol% propane-air mixtures at a temperature of 523 K and 548 K. At a temperature of 548 K the reproducibility is reasonable, while at a temperature of 523 K the reproducibility is rather poor. This poor reproducibility can be explained by the remaining soot and other reaction products that stay behind from previous experiments in spite of the abundant purging with compressed air. These reaction products decrease the ignition delay times and consequently facilitate auto-ignition. This influence is more significant at low temperatures and elevated pressures. A second explanation for the poor reproducibility is the material effect (see Section 2.1.5). A rust layer was formed at the insides

55

4.3 Auto-ignition limits of butane/air mixtures

2.5

First series


2

Second series Third series

1.5

1

0.5

0 520

530

540

550

560

570

580


Figure 4.4: The reproducibility of the determination of the auto-ignition limit for a 40 mol% propane in air mixture.

of the buffer vessel and the explosion vessel. This could explain the long term shifting of the auto-ignition limit.

4.3

Auto-ignition limits of butane/air mixtures

The second fuel for which the auto-ignition limits are determined is butane. Since butane has a longer chain length than propane, the auto-ignition temperature is expected to decrease. First the auto-ignition limit is determined for n-butane/air and i-butane/air mixtures separately in order to assess the influence of branching. Secondly two LPG mixtures are tested. By comparing the auto-ignition limits of the LPG-mixtures with the auto-ignition limits of the pure components, the influence of the different components to the auto-ignition behaviour can be estimated.

4.3.1

Auto-ignition limits of n-butane/air mixtures

Figure 4.6 presents the auto-ignition limits of n-butane/air mixtures for concentrations from 10 mol% up to 70 mol% n-butane and for temperatures from 503 K to 548 K (230 ◦ C to 275 ◦ C). The auto-ignition limits are determined with constant vessel temperature and varying pressure with a maximum pressure step-size of 0.05 MPa. The auto-ignition criterion is again a combined temperature ( > 50 K) and relative pressure rise ( > 10%) criterion within a

56


Equivalence ratio [-] 0

10

5

40

20


2.5 523 523 548 548 573

2

K first series K third series K first series K third series K first series

1.5

1

0.5

0 0

10

20

30

40

50

60

70

80

Molar fraction propane [mol%]

Figure 4.5: Influence of fuel concentration on the auto-ignition limit of propaneair mixtures with equivalence ratio equal to the actual fuel/air ratio divided by the stoichiometric fuel/air ratio.

time span of fifteen minutes. It can be seen that the auto-ignition temperatures are lower in comparison with the auto-ignition limits of propane of figure 4.5. As can be seen in figure 4.6, the auto-ignition limits decrease significantly with increasing concentration in the low concentration region. The concentration most sensitive to auto-ignition increases from 30 mol% at a temperature of 548 K to 60 mol% at a temperature of 511 K. At a temperature of 503 K the concentration most sensitive to auto-ignition could not be determined because of the saturation pressure of n-butane. The influence of pressure and temperature on the ignition delay times for a 50 mol% n-butane/air mixture is shown in figure 4.7. At a temperature of 548 K the ignition delay times are smaller than 200 seconds. Consequently the auto-ignition criterion at this temperature is the temperature or pressure rise. The ignition delay times increase with decreasing temperature. At a temperature of 523 K and 511 K the ignition delay time shows a steep decrease with increasing initial pressure. At a temperature of 511 K and 503 K the maximum ignition delay time of fifteen minutes is the determining criterion. At a temperature of 503 K the ignition delay time decreases less with increasing pressure. Consequently the auto-ignition limit at elevated pressure and low temperature is not well defined, because a shift of the ignition delay times cause a large shift of the auto-ignition limit.

57


2.5

503 K 511 K


2

523 K 1.5

548 K

1

0.5

0 0

10

20

30

40

50

60

70

80

Molar fraction n-butane [mol%]

Figure 4.6: Influence of fuel concentration on the auto-ignition limit of n-butane/air mixtures.

1200

503 K 511 K

1000

Ignition delay time [s]

523 K 548 K

800

600

400

200

0 0

0.5

1

1.5

2

2.5


Figure 4.7: Ignition delay times as function of the initial pressure determined for 50 mol% n-butane in air mixture.

58


2 1.8

523 K


1.6

536 K

1.4

548 K 1.2

573 K

1 0.8 0.6 0.4 0.2 0 0

10

20

30

40

50

60

70

Molar fraction iso-butane [mol%]

Figure 4.8: Influence of fuel concentration on the auto-ignition limit of iso-butaneair mixtures.

4.3.2

Auto-ignition limits of i-butane/air mixtures

Figure 4.8 presents the auto-ignition limits of i-butane/air mixtures for concentrations from 4 mol% up to 70 mol% iso-butane and for temperatures from 523 K to 573 K (250 ◦ C to 300 ◦ C). The concentration most sensitive to auto-ignition is not dependent on temperature and is equal to 50 mol%. The auto-ignition limits of iso-butane are comparable with the auto-ignition limits of propane, while the auto-ignition limits of n-butane are significantly lower. This can be explained by the chemical structure of the different alkanes. It requires more energy to break a CH3 radical from a branched alkane than from a straight alkane (see Section 2.1.2).

4.3.3

Auto-ignition limits of LPG/air mixtures

The first LPG-mixture investigated is a mixture of 2 components of which the auto-ignition limits differ the most, namely 50 mol% propane and 50 mol% n-butane. The auto-ignition limits are determined for a fuel concentration from 30 mol% to 70 mol% and for temperatures from 511 K to 536 K (238 ◦ C to 263 ◦ C) as can be seen in figure 4.9. The concentration most sensitive to auto-ignition increases with decreasing temperature. This is similar to the observations about propane and n-butane mixtures. The auto-ignition limits of the LPG mixture at a temperature of 523 K are compared with the autoignition limits of the individual components in figure 4.10. It is seen that the auto-ignition limits of the LPG mixture resemble best to the n-butane AIT limits. It can be concluded that the auto-ignition limits of the LPG mixture

59


2 1.8

511 K

1.6


517 K 1.4

523 K 1.2

536 K 1 0.8 0.6 0.4 0.2 0 20

30

40

50

60

70

80

Molar fraction LPG (50/50) [mol%]

Figure 4.9: Influence of fuel concentration on the auto-ignition limit of a LPG/air mixture containing 50 mol% propane and 50 mol% n-butane.

are in good agreement with the auto-ignition limits of the component with the lowest auto-ignition temperature. The second LPG mixture consists of three components: 40 mol% propane, 30 mol% n-butane and 30 mol% iso-butane. The auto-ignition pressures at a temperature of 523 K of two test series are presented in figure 4.11. Both series show a significant decrease of the auto-ignition pressure at a concentration of 60 mol%. The difference in the determination method between both test series is that for the first series the auto-ignition pressure is determined with decreasing pressure in contrast with the second test series where the autoignition limit is determined with increasing pressure. For the determination with decreasing pressure the auto-ignition limit is determined starting with an experiment at a high pressure at which auto-ignition occurs. In the following experiments the initial pressure is decreased step by step until an experiment is performed where no auto-ignition occurs. For the determination with increasing pressure the initial pressure of each successive experiment is increased until an experiment with an auto-ignition is observed. It is concluded that the combustion products of previous reactions could facilitate the auto-ignition in a following experiment. This effect was also observed with the propane/air mixtures (Section 4.2). In section 4.5 this influence will be researched in-depth for the methane/air mixtures. It can be concluded that two different auto-ignition limits are distinguished. The lowest limit determined with decreasing pressure is the safest auto-ignition limit for industrial purposes, while the highest limit determined with increasing pressure is of use for the auto-ignition modelling since the influence of soot is

60


2.5

AIT propane first series AIT propane third series


2

AIT LPG (50/50) AIT n-butane

1.5

1

0.5

0 10

20

30

40

50

60

70

80

Molar fraction fuel [mol%]

Figure 4.10: Comparison of the auto-ignition limits at a temperature of 523 K of LPG/air mixtures (LPG = 50 mol% propane and 50 mol% n-butane) with the auto-ignition limits of the pure components.

not yet included in the chemical kinetics modelling. Figure 4.12 gives a comparison between the auto-ignition limits of both LPG/air mixtures and n-butane/air mixtures at a temperature of 523 K. It is concluded that the minimum auto-ignition pressure does not differ significantly for the three mixtures. The concentrations that are most sensitive to auto-ignition seem to differ for the three mixtures. However it should be noted that the concentrations are presented as the total fuel concentrations and not as a function of the most sensitive component which is n-butane. A fuel concentration of 60 mol% LPG (50/50 propane/n-butane) corresponds with a n-butane concentration of 30 mol% and a fuel concentration of 60 mol% of the second LPG (40/30/30) mixture corresponds with 18 mol% n-butane. This explains why the auto-ignition limit of the second LPG mixture shows a sharp decrease at a fuel concentration of 60 mol% while the decrease for n-butane starts below 20 mol%. The auto-ignition limits increase for both LPG mixtures from a fuel concentration of 70 mol% because of the oxygen deficiency.

61


1.2

First series: decreasing pressure Second series: increasing pressure


1

0.8

0.6

0.4

0.2 20

30

40

50

60

70

80

Molar fraction LPG (40/30/30) [mol%]

Figure 4.11: Influence of fuel concentration on the auto-ignition limit of a LPG mixture containing 40 mol% propane, 30 mol% n-butane and 30 mol% iso-butane.

1

AIT LPG (40/30/30)

0.9

AIT LPG (50/50) Initial pressure [MPa]

0.8

AIT n-butane

0.7

0.6

0.5

0.4

0.3

0.2 10

20

30

40

50

60

70

80

Molar fraction fuel [mol%]

Figure 4.12: Comparison of the auto-ignition limits of two LPG/air mixtures with the auto-ignition limits of n-butane/air mixtures at a temperature of 523 K.

62


70 UFL 3.0 MPa

Molar fraction C3H8 [mol%]

60

UFL 2.0 MPa 50

UFL 1.5 MPa UFL 1.0 MPa

40


30

UFL 0.1 MPa 20

AIT 1.0 MPa AIT 1.5 MPa

10 0 280

330

380

430

480

530

580

630

Temperature [K]

Figure 4.13: Comparison between the upper flammability limits and the autoignition limits of propane/air mixtures.

4.4

Comparison between the auto-ignition limits and the upper flammability limits of propane and n-butane in air mixtures

The upper flammability limit (UFL) is the upper concentration limit of a mixture of a combustible gas and an oxidiser below which a flame is able to propagate independently (See also Figure 2.2 in Section 2.1.3). This section will describe the transition area from the upper flammability limit to the autoignition area for propane/air and n-butane/air mixtures. Figure 4.13 shows the temperature and pressure dependence of the upper flammability limit of propane/air mixtures determined in the 8 l buffer vessel. The auto-ignition limits for a pressure of 1.0 and 1.5 MPa are also shown on figure 4.13. These curves are interpolated from the auto-ignition data described in the previous section. The error bars indicate the scattering of the auto-ignition limit of the different test series. Although a large variation on the auto-ignition pressure for the different test series was measured (Figure 4.5), the error on the autoignition temperature is restricted to maximum 9 K. The upper flammability limits are determined according to the European standard EN 1839 (2003) with a 5% pressure rise as flammability criterion. In general the upper flammability limit shows a linear increase with increasing temperature as was suggested by Zabetakis et al. (1965). At a temperature of 523 K and at pressures from 0.5 MPa to 1.5 MPa a more than linear increase is observed with increasing temperature (see figure 4.13). This was also observed in a previous study by Van den Schoor and Verplaetsen (2006), who attributed this deviation to the proximity of the auto-ignition area. The upper flammability limit at a tem-

63

4.4 Comparison between the AIT and the UFL

70

Molar fraction n-butane [mol%]

UFL 2.0 MPa 60 UFL 1.5 MPa 50

UFL 1.0 MPa

40


30

UFL 0.1 MPa 20 AIT 0.6 MPa 10 0 280

330

380

430

480

530

580

630

Temperature [K]

Figure 4.14: Comparison between the upper flammability limits (UFL) and the auto-ignition limits (AIT) of n-butane/air mixtures.

perature of 523 K and a pressure of 1.0 MPa lies just outside the auto-ignition range of 1.0 MPa, while the upper flammability limit at 523 K and 1.5 MPa is located inside the auto-ignition range of 1.5 MPa. Consequently at 1.5 MPa a mixture with a concentration beyond the upper explosion limit can react spontaneously. Thus, this mixture does not support flame propagation after ignition, but auto-ignites after a time period of more than 2 minutes, which is the typical duration of a test for the determination of flammability limits. This might seem contradictive, but can be explained by the underlying phenomena. Propagation of a flame requires not only a fast chemical conversion, but also a high heat and mass transfer rate, whereas auto-ignition is initially primarily governed by chemistry and a slow heat transfer rate. Therefore, it is possible for a mixture which is too rich to sustain flame propagation, to have auto-ignition. Figure 4.14 presents the upper flammability limits of n-butane obtained by Van den Schoor and Verplaetsen (2006). These flammability limits are measured in a 4.2 l vessel with a flammability criterion of 1% relative pressure rise. Van den Schoor (2007) has shown that the flammability limits obtained with these conditions are in good agreement with the flammability limits according to the EN 1839 (2003). The upper flammability limit shows a linear increase with increasing temperature. The slope of the curves increases with increasing pressure. At a pressure of 0.6 MPa a deviation from the linear increase is observed at a temperature of 473 K. At a temperature of 523 K the upper flammability limit was not determined, but it was found that the mixture with a concentration of 66 mol% n-butane at 523 K and 0.6 MPa was still flammable. When the flammability limits are compared with the auto-ignition range, see figure 4.14, it can be seen that this last condition lies beyond the auto-ignition

64


temperature of n-butane at a pressure of 0.6 MPa. This explains why the upper flammability limit shows a significant increase at a temperature of 523 K and a pressure of 0.6 MPa. Two conclusions can be drawn from these comparisons. A first conclusion is that a mixture which is too rich to sustain flame propagation, still can auto-ignite. A second conclusion from these experiments is that the linear temperature dependence of the upper flammability limit as suggested by Zabetakis et al. (1965) is not valid for temperatures close to the auto-ignition area of the gas mixture.

4.5

Auto-ignition limits of methane/air mixtures

Caron et al. (1999) determined the auto-ignition limits of methane/air mixtures at elevated pressures and for methane concentrations from 30 to 80mol%. These experiments were performed in the same experimental set-up as used for this study, which is the closed vessel of 8 litres. The top part of figure 4.15 shows the three regimes that were identified by Caron et al. (1999). When no pressure or temperature increase was observed within 10 min, the attempt was considered unsuccessful and the test is considered not to give rise to an explosion. When both a pressure rise and a temperature rise larger than 200 K are recorded, auto-ignition has taken place. A temperature rise between 50 K and 200 K with a maximum pressure ratio of two or less was classified as a slow combustion. In contrast with Caron et al. (1999) who called this phenomenon a cool flame, it is preferred to identify it as a slow combustion, since no visual proof of the presence of cool flames was given. For this study, it is important to have insight into the thermodynamic phenomena that are responsible for the auto-ignition or that occur during the auto-ignition. Therefore new experimental data are needed. In order to measure the thermal gradients inside the explosion vessel three exposed thermocouples were used instead of one ungrounded thermocouple as used by Caron et al. (1999). The thermocouples were located at the centre, 6 cm above the centre and at the top of the vessel. First a new series of experiments was performed with a methane concentration of 60 mol% or an equivalence ratio of 14.3 and at a temperatures from 653 K to 713 K. In the bottom part of figure 4.15 these experiments are compared with previous experiments from Caron et al. (1999) . The same ignition criteria are used for the new experimental data. It can be seen that the results of this study are in good agreement with the auto-ignition limits of Caron et al. (1999). However no slow combustion area was observed in this study. This difference can be explained by the type of thermocouples that were used in both experimental set-ups. Caron et al. (1999) used one ungrounded thermocouple, which means that the thermocouple junction is detached from the probe wall, in the centre of the vessel with a diameter of 1 mm, while in this study three exposed thermocouples with a diameter of 0.5 mm are used. These thermocouples are capable of following steep temperature rises and can measure consequently higher temperatures than the 1 mm thermocouple (see

4.5 Auto-ignition limits of methane/air mixtures

65

Section 3.3). A disadvantage of the exposed thermocouples is that they are fragile and that they can be destroyed by a severe explosion. Figure 4.16 shows that the sequence of testing can have a major influence on the value of the auto-ignition limit. The first two experiments with an initial pressure of 0.4 and 0.94 MPa do not lead to an auto-ignition. At a pressure of 1.22 MPa auto-ignition occurs. The following experiments with decreasing initial pressure also ignite spontaneously. Only at an initial pressure of 0.43 MPa no reaction occurs. Two auto-ignition limits can be distinguished from figure 4.16. The auto-ignition pressure determined at 713 K and increasing pressure is 0.94 MPa whereas for decreasing pressure the auto-ignition pressure is only 0.43 MPa. This last pressure is also in good agreement with the slow combustion limit of Caron et al. (1999). Repeated testing could lower the auto-ignition limit determined with decreasing pressure. Because of the poor reproducibility and the differences on the auto-ignition limit a new testing procedure is developed, which is discussed next. The standard testing procedure between two successive experiments consists of three steps. Firstly, the explosion vessel is emptied. Secondly the explosion vessel is flushed with compressed air for 2 minutes and then put under vacuum. Thirdly, the buffer vessel is filled to its initial pressure. During an auto-ignition reaction products and soot are formed. If these products are not completely removed from the explosion vessel, they can facilitate the auto-ignition in following experiments. A first modification to the testing procedure is that after the evacuation of the reaction products and the flushing with air, the vessel is brought to vacuum and filled with pure oxygen to an absolute pressure of 0.2 MPa. The pure oxygen accelerates the oxidation of any remaining products. After this the vessel is emptied and flushed with compressed air. After this modification, there was still some interference between successive experiments. This was because of the residence time of the gas mixture in the buffer vessel. Because the buffer vessel was not emptied between two successive experiments a part of the gas mixture stayed for longer time in the buffer vessel. This might lead to pre-oxidation reactions. To avoid these reactions, the temperature of the buffer vessel was lowered to room temperature instead of 373 K. This modification did not lead to the desired outcome. When the buffer and the explosion vessel were opened, a layer of rust was detected in the buffer vessel and a layer of soot and rust was detected in the explosion vessel. The vessels were cleaned by sandblasting the inner surfaces of the vessels. In the last test series the buffer vessel was also emptied and refilled between two successive experiments resulting in a significant improvement of the repeatability. At a temperature of 683 K the auto-ignition pressure of a 60 mol% methane in air mixture has been determined four times with increasing and decreasing pressure by following the new testing procedure and resulted in an average auto-ignition pressure of 1.55 MPa with a standard deviation of 0.05 MPa. It can be concluded that the new testing procedure improves the repeatability significantly. Figure 4.17 makes the comparison between the data of Caron et al. (1999) and the data obtained by this study for different methane concentrations and at a temperature of 683 K. Three observations can be made:

66


A 6 Auto-ignition Slow combustion No reaction Auto-ignition limit Slow combustion limit


5

4

3

2

1

0 600

620

640

660

680

700

720


B 5 Auto-ignition (this study) No reaction (this study)


4

AIT limit (this study) AIT Caron et al. (1999)

3

Slow Combustion Caron et al. (1999)

2

1

0 600

620

640

660

680

700

720


Figure 4.15: Initial temperature-initial pressure diagrams for the slow combustion and the auto-ignition region, determined at 60 mol% methane in air: (A) data from Caron et al. (1999), (B) data obtained in this study.


67


1.4 no reaction auto-ignition

1.2 1.0 0.8 0.6 0.4 0.2 0.0 1

2

3

4

5

6

7

8

9

Number of experiment

Figure 4.16: Sequence of auto-ignition experiments with a 60 mol% methane/air mixture and a vessel temperature of 713 K.

• The slow combustion range is smaller for the new data. As can be seen on figure 4.17, in the data from Caron et al. (1999) the slow combustion region starts from a concentration of 50 mol%, while for the new data only slow combustions are observed from a concentration of 70 mol%. This can be explained by the differences in thermocouples that are used in both experimental set-ups. In the new experiments three exposed thermocouples are used instead of one ungrounded thermocouple. These exposed thermocouples have a smaller time constant and are able to measure higher temperatures, see section 3.3. It is also observed that the slow combustions of this study had a maximum temperature rise of more than 100 K and a relative pressure rise of more than 10%. Consequently these slow combustions would be classified as auto-ignitions following the ignition criterion for propane and butane mixtures (see Section 3.2). • The auto-ignition limits of this study are in general higher than the limits obtained by Caron et al. (1999). These large differences in auto-ignition limits can be explained by the differences in the experimental procedure. The new data are obtained following the improved testing procedure, which shows no influence if the determination is performed with increasing or decreasing pressure. The experiments of Caron et al. (1999) are obtained with decreasing pressure and it is seen in figure 4.16 that this determination method could significantly lower the auto-ignition pressure. • Despite the differences in experimental method it can be expected that the concentration most sensitive to auto-ignition (70 mol%) remains the same, which is confirmed by the results. Up to now only the auto-ignition limits of the methane/air experiments are presented. Supplementary information can be obtained from the temperature measurements by the three exposed thermocouples that are used for the experiments with methane/air mixtures. Figure 4.18 presents the temperature

68


A 3.0 Auto-ignition Slow combustion No reaction AIT limit SC limit


2.5

2.0

1.5

1.0

0.5

0.0 20

30

40

50

60

70

80

90

100

Methane molar fraction [mol%]

B 3.0

Auto-ignition Slow Combustion No reaction


2.5

2.0

1.5

1.0

0.5

0.0 20

30

40

50

60

70

80

90

100


Figure 4.17: Concentration-initial pressure diagrams for the slow combustion and the auto-ignition region, determined at a temperature of 683 K: (A) data from Caron et al. (1999), (B) data obtained in this study.

69


2

1100 Top Temp

1050

Elevated Temp Central Temp

950

1.5

Pressure

900 1

850 800 750

Pressure [MPa]

Temperature [K]

1000

0.5 700 650 600

0 0

10

20

30

40

50

60

70

Time [s]

Figure 4.18: Recorded pressure and temperature histories of a test at 713 K and 1.2 MPa of a 60 mol% methane/air mixture ("Top Temp" represents the temperature at the top of the vessel while "Elevated Temp" and "Central Temp" respectively represents the temperature 6 cm above and at the centre of the vessel).

and pressure histories of an experiment at a wall temperature of 713 K and an initial pressure of 1.2 MPa. It can be seen that during the inflow of the gas mixture the temperature inside the explosion vessel decreases with 30 K. After closing the inlet the temperature of the gas starts to increase. After 20 seconds the temperature has reached the temperature of the wall. This period of time is relatively small in comparison with the total time of 10 to 15 minutes in which explosions are observed. In this experiment the explosion starts at 59 s, which is 46 s after the closing of the vessel. Before the beginning of the explosion, the temperature of the gas mixture slightly increases and from 45 s onwards the temperature at the top and the temperature at 6 cm above the centre increase more than the temperature at the centre of the vessel. From 59 s onwards the temperature at the top of the vessel increases exponentially and thereafter with an interval of about 1 second also the temperature at 6 cm above the centre and at the centre starts to increase. From this measurement it can be concluded that because of the natural convection the auto-ignition starts at the top of the vessel and propagates downwards through the rest of the volume. This observation will also be confirmed by the simulation results which will be presented in the following chapter.

70


Chapter 5

Numerical study of the auto-ignition of alkane/air mixtures When I have an idea, I turn down the flame, as if it were a little alcohol stove, as low as it will go. Then it explodes, and that is my idea. Ernest Hemingway, American novelist (1899 – 1961)

T his section describes the modelling of the auto-ignition of the alkane/airmixtures that were investigated in the experimental part of this study. The

modelling is based upon detailed chemical kinetics and different heat transfer models. This chapter starts with a short overview of the auto-ignition modelling available in literature (Section 5.1.1). In addition the numerical methods are described. First a zero-dimensional approach is adopted based upon the model of Semenov. The chemistry is based upon a detailed reaction mechanism. In order to model the heat transfer and convective flows more accurately a 1-D and 2-D model are developed. In section 5.2 the numerical results for the methane/air mixtures will be presented and compared with the experimental data. Finally, in section 5.3 the numerical results for propane/air mixtures calculated with the 0-D model are presented and compared with the experimental data.

5.1 5.1.1

Numerical method Background on auto-ignition modelling

In section 2.3 the theoretical auto-ignition models of Semenov and FrankKamenetskii were described. Over the last decades, because of the increased

71

72

Chapter 5 Numerical study of the auto-ignition

computer performance, numerical modelling has gained in importance as a new approach to study the auto-ignition behaviour of gas mixtures (Gkagkas and Lindstedt (2007), Minetti et al. (1995), Stauch and Maas (2007)). Nevertheless, it is not yet feasible to include a detailed chemical kinetics mechanism with hundreds of reactions and tens of species in a transient three-dimensional (3-D) computational fluid dynamics (CFD) simulation, as would be required to determine the auto-ignition temperature in complex geometries. There are, however, several simplifications possible to model the auto-ignition process. Firstly, the detailed chemical kinetics can be solved in a zero-dimensional (0D) or in a one-dimensional (1-D) model (Buda et al., 2006). These models are based upon the work of Semenov (1935) and Frank-Kamenetskii (1955). This approach leads to a strong reduction of the calculation time. However, this is only suited for the modelling of auto-ignition phenomena with negligible spatial gradients — for example, in well stirred reactors (Hughes, 2006). Secondly, the detailed chemical kinetics can be reduced and solved in a CFD code (Campbell et al., 2007; Foster and Pearlman, 2006; Griffiths, 1995). This method requires a strong reduction of the reaction mechanisms to keep the calculation time within acceptable limits. Thirdly, the chemical kinetics and the flow simulation can be treated separately. For example, in the Shell autoignition model (Shell Global Solutions, 2001) the temperature profile along a streamline is first calculated for a non-reactive flow by means of a CFD code and it is subsequently used when solving the detailed chemical kinetics in a zero-dimensional model. The main drawback of this last approach is that there is no direct interaction between the chemical kinetics and the flow simulation.

5.1.2

Mathematical model

A complete model of the auto-ignition process has to include fluid dynamics and transport phenomena together with detailed chemical kinetics. The mathematical model consists of four governing equations: mass, momentum, energy and species conservation. A derivation of these equations can be found in (Williams, 1985). • Mass conservation:

∂ρ − + ∇ · (ρ→ v)=0 ∂t − with ρ the mass density, t time and → v the mixture velocity.

(5.1)

• Energy conservation: ρ

N X ← → → − ∂u − − − − + ρ→ v · ∇u = −∇ · → q − P : (∇→ v)+ρ Yi → gi · Vi ∂t i=1

(5.2)

← → − with u the internal energy per unit mass, → q the heat flux vector, P the → − stress tensor, Yi the mass fraction of species i, gi the gravitational force → − per unit mass on species i and Vi the diffusion velocity of species i.

73

5.1 Numerical method

− The heat flux vector → q is given by: → − q = −λ∇T + ρ

N X

N X N X → − − − → Xj DT,i → hi Yi Vi + RT Vi − Vj Wi Dij i=1 i=1 j=1

(5.3)

with λ the thermal conductivity, hi the specific enthalpy of species i, R the universal gas constant, DT,i the thermal diffusion coefficient of species i and Wi the molar mass of species i. This equation states that the heat flux is the result of thermal conduction, species diffusion and concentration gradients (the Dufour effect). The radiant heat flux is neglected in the calculations. The stress tensor is given by: h i ← → ← → 2 T → − − − µ − µb ∇ · v U − µ ∇→ v + (∇→ v) P = p+ 3

(5.4)

with p the hydrostatic pressure, µ the dynamic viscosity and µb the bulk viscosity. The diffusion velocities can be calculated from: N X − → − Xi Xj → ∇p V j − V i + (Yi − Xi ) ∇Xi = Dij ρ j=1 N

+

+

→ − → − ρX Yi Yj f i − f j p j=1 N X Xi Xj DT,j j=1

ρDij

Yj

−

DT,i Yi

∇T T

i = 1, ..., N (5.5)

with Xi the molar fraction of species i, Dij the binary diffusion coefficient of species i and j, DT,i the thermal diffusion coefficient of species i and T the absolute temperature. This equation states that concentration gradients are supported by diffusion velocities, pressure gradients, differences in the external forces on different species and temperature gradients (the Soret effect). The numerical simulations of this study have shown that neglecting the Soret effect (thermal diffusion) did not alter the auto-ignition limits of the methane/air mixtures. • Momentum conservation: N − X ← → ∂→ v − − − +→ v · ∇→ v = −∇ · P /ρ + Yi → gi ∂t i=1

(5.6)

• Species conservation: ρ

→ − ∂Yi − = −ρ→ v · ∇Yi + ω˙ i − ∇ · ρYi Vi ∂t

i = 1, ..., N.

(5.7)

74


The chemical kinetics enter these equations via the species rate of production ω˙ i . Since the chemical kinetics play an important role in the auto-ignition process, different reaction mechanisms will be used in the calculations, as described in the next section.

5.1.3

Reaction mechanisms

Hydrocarbons are a family of compounds for which a number of detailed reaction mechanisms exist (Simmie, 2003). However, most of these mechanisms are only valid for high temperature combustion (> 1000 K). Kinetic data and mechanisms for the low temperature region are scarce (Pilling, 1997). The main problem is the lack of quantitative experimental data for the rate constants of elementary reactions in the low temperature region. For the numerical study of methane, the results of four different reaction mechanisms are compared with the experimental auto-ignition data of methane-air mixtures. These mechanisms are the GRI 3.0 (Gas Research Institute) mechanism (Frenklach et al., 1994), the C1–C2 reaction database of the L’Ecole Nationale Supérieure des Industries Chimiques (ENSIC) (Barbé et al., 1995), the hydrocarbon mechanism of the National Institute of Standards and Technology (NIST) (Babushok et al., 1995) and a mechanism for methane oxidation of the British Gas Corporation (BGC) proposed by Reid et al. (1984). These reaction mechanisms are summarised in table 5.1. The GRI 3.0 mechanism is optimised for methane and natural gas oxidation for temperatures by fitting the reaction rate parameters to a variety of experimental data. The C1–C2 reaction database of the ENSIC has been developed through automatic generation and it is validated with methane and ethane oxidation experiments in a jet-stirred reactor. The hydrocarbon mechanism of the NIST includes 240 reactions and 34 species for the oxidation of methane and ethane for temperatures in the range 900–2000 K and pressures in the range 0.05–0.15 MPa. The mechanism of the BGC has been developed to model the spontaneous ignition of methane by a hot surface in stirred and unstirred vessels. A detailed description of these reaction mechanisms can be found in their respective references. For the numerical study of propane, six kinetic reaction mechanisms are compared. Table 5.2 summarises these mechanisms. The first five have been published (San Diego Mechanism (2003), Westbrook (1984), Sung et al. (1998), Qin et al. (2000), Koert et al. (1996)), while the last one is part of the software package Exgas-Alkanes of Battin-Leclerc (2004).

5.1.4

0-D model

As a first approach, in order to choose the most appropriate reaction mechanism, we focus on the chemistry of the auto-ignition process by applying a physical model that includes a detailed reaction mechanism but neglects diffusion and convection. For this zero-dimensional model, the equations 5.1–5.7

Number of species 53 63 34 21

Number of reactions 325 439 240 55

Temperature range of 1000–2500 K 773–1573 K 900–2000 K 900 K

Pressure range 0.001–1 MPa 0.1 MPa 0.05–0.15 MPa 0.1 MPa

Table 5.1: Summary of the reaction mechanisms for methane oxidation.

Reaction mechanism GRI 3.0 (Frenklach et al., 1994) ENSIC (Barbé et al., 1995) NIST (Babushok et al., 1995) BGC (Reid et al., 1984)

5.1 Numerical method 75

Number of reactions 173 168 621 463 689 713

Number of species 39 36 92 70 155 118

Based on experimental data of Rapid Compression shock tube (0.1-3 MPa) Propane and propene oxidation and pyrolysis Counterflow diffusion flames (0.1-1.5 MPa) Rapid compression flames (0.1-1.5 MPa) High pressure flow reactor (650-800 K, 0.1-1.5 MPa) Low temperature oxidation

Table 5.2: Summary of the reaction mechanisms for propane oxidation.

Reaction mechanism San Diego San Diego Mechanism (2003) Westbrook Westbrook (1984) Princeton Sung et al. (1998) Delaware Qin et al. (2000) Koert and Pitz Koert et al. (1996) EXGAS-Alkanes Battin-Leclerc (2004)

Rich mixtures till 16 mol% 2.05-7.73 mol% (φ = 0.5-2) 1.65 mol% (φ=0.4) till 16 mol% Unknown

Concentration range 2.05-7.73 mol% (φ = 0.5-2) Unknown

76 Chapter 5 Numerical study of the auto-ignition


reduce to

77

N

∂T qloss X ρcv = − hi ω˙ i ∂t V i=1

(5.8)

∂Yi = ω˙ i i = 1, ..., N. (5.9) ∂t with cv the specific heat capacity at constant volume and V the internal volume. The heat loss to the wall of the vessel qloss is assumed to be convective, i.e. proportional to the gas-wall temperature difference: ρ

qloss = h · S · (T − Tw )

(5.10)

with h the convective heat transfer coefficient, S the internal surface area, and T and Tw the temperature of the gas and of the wall, respectively. Here, h is taken to be 5 W/m2 K. The choice of this value will be clarified in Section 5.2.1. The internal surface area S is 1932 cm2 , which corresponds to the surface of a sphere with an internal volume V of 8 dm3 . This model is implemented in Chemkin 4.0.2 (Kee et al., 2005) as a homogeneous batch reactor. In order to obtain the evolution of the temperature and of the species concentrations in time, the system of partial differential equations must be solved by numerical integration methods. This system is generally stiff because of the chemical kinetics and it is most efficiently solved by implicit techniques for time integration. For this purpose, Chemkin uses the software package DASPK (Li and Petzold, 2000).

5.1.5

1-D and 2-D CFD-Kinetics model

In order to simulate the diffusive and convective heat transfer more accurately, a one-dimensional and a two-dimensional model are implemented. The 1-D model is able to describe the auto-ignition process in a spherical explosion vessel while neglecting the effect of buoyancy, whereas the 2-D model is able to take buoyancy into account in an axisymmetric explosion vessel. In order to model the spherical auto-ignition vessel, an axisymmetric spherical geometry with symmetry around the vertical axis is used in the calculations. The 1-D model is derived from the 2-D model by eliminating the gravity forces. This results in a spherically symmetric or 1-D simulation. The model is solved as a transient problem using the Fluent code (Release 6.3.26 2006). In Fluent the control volume method — sometimes referred to as the finite volume method — is used to discretise the transport equations. The total number of grid cells is 1400 and 5400 for the 1-D and the 2-D model, respectively. The composition of the 2-D grid is presented in figure 5.1. Only half of a circle is modelled. The x-axis is the symmetry axis and the gravity force lies according to the opposite direction of the x-axis. The grid independence was checked by performing simulations with the number of grid cells doubled. The fluid is treated as fully compressible because the temperature and pressure rise can be considerable during auto-ignition. The density is calculated by the

78


X Y

g

Figure 5.1: Numerical grid for the 2-D spherical simulations.

ideal gas law. The pressure is handled as a floating operating pressure to account for the slow changing of the pressure without using acoustic waves. The flow is assumed to be laminar because the buoyancy driven velocities are small (∼ 10 cm/s) and the Rayleigh number (see equation 5.13 on page 88) does not exceed 108 (Bejan, 2004). The fluid temperature at the wall is required to be equal to the wall temperature. This temperature is also the initial temperature of the gas mixture. The chemistry is calculated and coupled to the flow calculations by means of a KINetics plug-in from Reaction Design. This technology couples Reaction Design’s KINetics chemistry-solver module (Kee et al., 2005) to the flow simulation of Fluent. For transient analyses, the solvers are coupled using an operator-splitting method. With this method, the species and energy conservation calculations are performed in two half time steps for each time step, where the KINetics solver determines the change in time due to the chemistry and Fluent determines the change in time due to fluid and heat transport. The time-step size was varied in the range 0.01–1 s to achieve results that are independent of the time step size.

5.1.6

Auto-ignition criterion

In order to determine the auto-ignition limits of a mixture, the calculated temperature-time profiles are interpreted in the same way as the experimental

79


Figure 5.2: Temperature histories for a 60 mol% methane-air mixture at an initial temperature of 623 K and varying initial pressure from 2 MPa to 1.4 MPa using the 1-D model with the BGC-mechanism.

profiles of this study. For the methane/air mixtures if the (maximum) temperature rises at least 200 K within a period of 10 minutes, an auto-ignition is said to have occurred. This corresponds exactly with the experimental criterion. For the propane and n-butane simulations the auto-ignition criterion is a maximum temperature rise of 50 K within a duration of fifteen minutes as in the experiments. The auto-ignition pressures, presented in section 5.2, are determined with an accuracy of 0.01 MPa for the zero-dimensional model, while for the 1-D and 2-D CFD model calculations, which are far more time-consuming, an accuracy of 0.1 MPa is obtained for the high pressures and 0.05 MPa for the low pressures. As an example, figure 5.2 shows the temperature-time profiles of different 1-D simulations at different initial pressures at an initial temperature of 623 K of a methane/air mixture. The induction time, i.e. the time before an auto-ignition appears, decreases with increasing pressure. The calculations at initial pressures of 2.0, 1.8 and 1.6 MPa resulted in induction times of 370 s, 470 s and 640 s, respectively. At an initial pressure of 1.4 MPa the maximum temperature rise was only 43K after 900 s. According to the above mentioned auto-ignition criterion, the simulations with an initial pressure of 1.4 and 1.6 MPa are classified as no ignitions. Consequently, the auto-ignition limit at 623 K is 1.6 MPa.

80


5 NIST 0-D model GRI 3.0 0-D model BGC 0-D model ENSIC 0-D model AIT of this study AIT Caron et al. (1999) SC Caron et al. (1999)

Pressure [MPa]

4

3

2

1

0 580

600

620

640

660

680

700

720

740

Temperature [K]

Figure 5.3: Comparison between experimentally and numerically determined autoignition limits (0-D) of methane-air mixtures: pressure dependence of the autoignition limit determined at 60 mol% methane in air.

5.2

Numerical results of methane/air mixtures

This paragraph contains the comparison between the experimental auto-ignition data for methane/air mixtures and the computed data. First the results of the zero-dimensional model are considered. This model assumes a homogeneous composition and a uniform temperature over the entire volume. Afterwards the results of the one-dimensional and two-dimensional simulations are presented and discussed.

5.2.1

0-D model

The output of a zero-dimensional model typically consists of the time evolution of the pressure, the temperature and the species molar fractions. In figure 5.3 they are compared with data for a methane concentration of 60 mol% at initial temperatures of 623–713 K, while in figure 5.4 the calculated auto-ignition limits are compared with experimental data at an initial temperature of 683 K for methane concentrations of 30–80 mol%. As can be seen, there are large differences between the results of the different reaction mechanisms. Moreover, the agreement between the numerical results and the experimental data is rather poor. As expected the NIST mechanism which is mainly valid at high temperatures, gives values for the auto-ignition limit that are too high. The GRI mechanism gives a good prediction of the auto-ignition limit of this study at low pressures but has too steep an increase of the auto-ignition pressure at lower temperatures. For the GRI mechanism the concentration most sensitive to auto-ignition lies below 30 mol%, while the experimental data have a

81

5.2 Numerical results of methane/air mixtures

5

NIST 0-D model GRI 3.0 0-D model BGC 0-D model ENSIC 0-D model AIT of this study AIT Caron (1999) SC Caron (1999)

Pressure [MPa]

4

3

2

1

0 0

10

20

30

40

50

60

70

80

90


Figure 5.4: Comparison between experimentally and numerically determined autoignition limits of methane-air mixtures: concentration dependence of the auto-ignition limit at 683 K.

6

h=50 W/m²K h=20 W/m²K h=10 W/m²K h=5 W/m²K h=2 W/m²K AIT of this study AIT Caron et al. (1999) SC Caron et al. (1999)

Pressure [MPa]

5

4

3

2

1

0 600

620

640

660

680

700

720

Temperature [K]

Figure 5.5: Influence of the heat transfer coefficient on the numerically determined auto-ignition limits using the zero-dimensional model and the BGC reaction mechanism.

82


4

timecrit = 300s Pressure [MPa]

3

timecrit = 600s timecrit = 900s

2

1

0 600

620

640

660

680

700

720

Temperature [K]

Figure 5.6: Influence of the time criterion on the numerically determined autoignition limits using the zero-dimensional model and the BGC reaction mechanism.

minimum auto-ignition pressure at a concentration of 70 mol%. The ENSIC mechanism, mainly valid for the low temperature oxidation kinetics give values for the auto-ignition limit that are too low. Overall, the best agreement is found for the BGC mechanism, especially when the temperature dependence of the auto-ignition pressure is observed. Consequently, this mechanism will be used in the 1-D and 2-D calculations. The value of the heat transfer coefficient h was calculated from a correlation for natural convective flow round spherical volumes (Bejan, 2004). h=

Nu · λ 0.589Ra1/4 with N u = 2 + D [1 + (0.469/P r)9/16 ]4/9

(5.11)

with N u the Nusselt number, Ra the Rayleigh number, P r the Prandtl number, λ the thermal conductivity and D the diameter of the vessel. For a 60 mol% methane in air mixture with a temperature difference of 1 to 200 K between the gas and the wall the heat transfer coefficient has a value between 2 and 8 W/m2 K. h is taken equal to 5 W/m2 K for the calculations of figures 5.3– 5.4. Since this coefficient has to be estimated, the influence of its value on the calculated auto-ignition limits is investigated, the results of which are shown in figure 5.5. As expected, an increasing value of the heat transfer coefficient results in a shift of the auto-ignition limit to higher temperatures. When focusing on the experimentally determined auto-ignition limits it can be seen that they are roughly located in the range h = 5 - 50 W/m2 K. The autoignition limit obtained in this study has an excellent agreement with numerical data obtained with a heat transfer coefficient of 50 W/m2 K. This value is unrealistically high for natural convection flows inside a closed vessel (Bejan, 2004). Therefore the heat transfer coefficient is chosen to be constant and


REDUCED BGC MECHANISM HIGH TEMP / LOW PRESSURE (15 species, 17 reactions)

BGC MECHANISM (21 species, 55 reactions)

CH4

CH4

+ HO2 / OH / H / O

CH3O2

+ O2

C2H6

CH3 + HO2 / OH

CH3O2H

CH3O CH2O

C2H5

CH3

+ CH3

CH3O + O2

C2H4

+ O2 + HO2 / CH3 / OH / H / O

HCO + HO2 / OH

+ HO2 / OH

+ HO2

+ O2 +M

CO2

83

+ O2 +M

CO

CH2O

C2H6 + OH / CH3

C2H5 + O2

C2H4

+ HO2 / CH3

HCO + O2

CO

Figure 5.7: Reaction path diagrams of the full and reduced mechanism of BGC.

equal to 5 W/m2 K for the numerical calculations of the 0-D model in order to compare objectively the different reaction mechanisms. Another parameter that has an influence on the auto-ignition limit is the ignition time criterion, as can be seen in figure 5.6. A decreasing time criterion increases the autoignition limit, but the influence is only noticeable at high pressures and low temperatures. Reduction of kinetic mechanism The BGC mechanism consisting of 55 reactions and 21 species was reduced by a former colleague, ir. L. Vandebroek, to a mechanism consisting of 17 reactions and 15 species by means of a rate of production analysis in order to reduce the calculation time for the 2-D model. The mechanism is reduced for the high temperature and low pressure region and is presented schematically in figure 5.7. As can be seen from the figure the reaction path along the peroxides, which is important for the high pressure region (Westbrook, 2000), is removed in the reduced mechanism. Figure 5.8 compares the auto-ignition limits calculated with the full and the reduced mechanism at 60 mol% methane in air. The auto-ignition limit obtained with the reduced mechanism deviates only at high pressure and low temperature from the limit obtained with the full mechanism. The reduced mechanism has a good agreement with the slow combustion limit of Caron et al. (1999) over the entire pressure range. However there is still a large difference with the experimental auto-ignition limits obtained in

84


5 Full BGC-mechanism Reduced BGC-mechanism AIT of this study AIT Caron et al. (1999) SC Caron et al. (1999)

Pressure [MPa]

4

3

2

1

0 620

630

640

650

660

670

680

690

700

710

720

Temperature [K]

Figure 5.8: Comparison of the numerically determined auto-ignition limits using the zero-dimensional model with the full and the reduced mechanism of the BGC.

this study. It can be concluded that it is possible to fit the zero-dimensional model to the experimental results by adapting the heat transfer coefficient or by adapting the reaction mechanism. The question should be put if the 0-D model will still be valid if other process conditions, such as the volume and the flow conditions, are changed. The main drawback of the zero-dimensional model is the simplicity of the heat transfer model due to the time-independency of the heat transfer coefficient and the necessity of experimental data to determine its value. The 1-D and 2-D models discussed next will simulate the heat transfer in more detail.

5.2.2

1-D model

The full mechanism of the British Gas Corporation (Reid et al., 1984) was incorporated in a one-dimensional (without the effect of buoyancy) computational fluid dynamics model. Contrary to the zero-dimensional model, there is no need to specify the value of the heat transfer coefficient h. The output of the calculations consists of the time evolution of the temperature, the pressure and the species molar fractions together with the spatial distribution of the temperature and the species molar fractions. An example of the temperature output is shown in figure 5.11 for a 60 mol% methane/air mixture at an initial temperature of 713 K and an initial pressure of 0.4 MPa. The temperature increases exponentially which leads to the auto-ignition of the gas-mixture after 80 s. Figure 5.9 shows the results of different simulations varying the initial pressure in order to find the auto-ignition limit at a certain temperature. The induction time, i.e. the time before auto-ignition appears, decreases with increasing pressure. Initial pressures of 0.6 to 0.3 MPa resulted in induction


85

Figure 5.9: Temperature histories for a 60 mol% methane/air mixture at an initial temperature of 713 K and varying initial pressure from 0.6 MPa to 0.15 MPa using the 1-D model.

times lower than 130 s. The induction time increases significantly to 300 s for an initial pressure of 0.2 MPa. At an initial pressure of 0.15 MPa the maximum temperature rise is only 13 K after 285 s. This run is classified as no ignition because the temperature rise is below 50 K. The auto-ignition limit at 713 K is consequently 0.15 MPa. Equivalent simulations were performed at temperatures of 673 K and 623 K and resulted in a respective auto-ignition limit of 0.4 and 1.6 MPa. Figure 5.10 compares the auto-ignition limit of the one-dimensional model with the zero-dimensional model. Strikingly, the results of the 1-D calculations deviate more from the experimental data than those of the 0-D calculations. However, it must be borne in mind that in order to perform the 0-D calculations a heat transfer coefficient h has to be specified a priori. As already shown in figure 5.5, the choice of this parameter largely influences the outcome of the calculation.

5.2.3

2-D model

A disadvantage of the zero- and the one-dimensional models is the absence of natural convection. The buoyant flow that arises after the birth of a hot kernel will increase the heat loss and consequently will increase the auto-ignition temperature. A two-dimensional model was developed to model the flow and the

86


5 0-D model 1-D model AIT of this study AIT Caron et al. (1999) SC Caron et al. (1999)

Pressure [MPa]

4

3

2

1

0 620

630

640

650

660

670

680

690

700

710

720

Temperature [K]

Figure 5.10: Comparison of the numerically determined auto-ignition limits using the BGC mechanism in the 0-D and the 1-D with the experimental data at 60 mol% methane in air.

reactions in a closed vessel. The same reaction mechanism (BGC) is used as in the one-dimensional model. Figure 5.12 shows an example of the spatial temperature field obtained with the 2-D model for a 60 mol% methane-air mixture at an initial temperature of 713 K and an initial pressure of 0.6 MPa. To obtain a better insight into the initial temperature increase, two different temperature scales have been used. Initially the temperature rise is homogeneous. After 20 seconds the location of the maximum temperature moves to the top of the vessel. After 50 seconds the auto-ignition starts at the top of the vessel and expands downwards to the entire volume of the vessel. The results of the 2-D calculations for the full and reduced BGC mechanism (see Section 5.2.1) are shown in figure 5.13. It can be seen that reduced mechanism overestimates the auto-ignition pressure at lower temperatures. The overall slope of the reduced mechanism is too steep in comparison with the experimental data. Consequently, although the time savings, the reduction of the reaction mechanism leads to a worse prediction of the auto-ignition limit with the 2-D model. In figure 5.14 the results of the 2-D calculations together with those of the 0-D and 1-D calculations for the full BGC mechanism are compared with the experimental data of this study. It can be concluded that the convective heat transfer — which is absent in the 1-D model — is important in the auto-ignition process and that, consequently, the constant value of h = 5 W/m2 K, which is used in the 0-D model, is a better estimate of the heat transfer coefficient than the one calculated when using the purely diffusive 1-D model. In order to compare the heat transfer in the 1-D and 2-D model with the heat transfer in the 0-D model an equivalent 0-D heat transfer coefficient is

87


760K

10 s

20 s

50 s

40 s

30 s

70 s

60 s

80 s

710K

Figure 5.11: Temperature history of a 60 mol% methane-air mixture at an initial temperature of 713 K and an initial pressure of 0.4 MPa using the one-dimensional model with the full BGC mechanism.

Figure 5.12: Temperature history of a 60 mol% methane-air mixture at an initial temperature of 713 K and an initial pressure of 0.6 MPa using the two-dimensional model with the full BGC mechanism.

5 0-D model full BGC 0-D model reduced BGC

Pressure [MPa]

4

2-D model full BGC 2-D model reduced BGC AIT of this study

3

AIT Caron et al. (1999) SC Caron et al. (1999)

2 1 0 620

630

640

650

660

670

680

690

700

710

720

Temperature [K]

Figure 5.13: Comparison between the full BGC mechanism and the reduced BGC mechanism in the 0-D and 2-D model.

88


5

0-D model 1-D model 2-D model AIT of this study

Pressure [MPa]

4

3

2

1

0 620

630

640

650

660

670

680

690

700

710

720

Temperature [K]

Figure 5.14: Comparison of the numerically determined auto-ignition limits using the full BGC mechanism in the 0-D, 1-D and 2-D model with the experimental data of this study at 60 mol% methane in air.

defined as: h=

qloss S · (Taverage − Tw )

(5.12)

The heat loss qloss is calculated by the CFD model as the total heat flux to the vessel wall. Figure 5.15 presents the evolution of the equivalent 0D heat transfer coefficient (equation 5.12) and the evolution of the average temperature of the 1-D and 2-D simulation. The heat transfer coefficient h decreases identically for both simulations during the first 20 seconds. From 20 seconds onwards, however, the two profiles diverge. The 1-D simulation, which does not include natural convection, shows a decreasing heat transfer coefficient. The 2-D simulation, on the contrary, shows an increasing coefficient because of the increasing natural convection caused by the temperature rise. This explains why the auto-ignition limit determined with the 1-D model is lower than that determined with the 2-D model. Another means of comparing the 1-D and the 2-D simulation is by comparing the temperature profiles (Figure 5.16). Initially, the temperature evolution is identical. After 30 seconds the maximum temperature in the 2-D simulation moves upwards. This results in a lower volume averaged temperature in the 2-D simulation than in the 1-D simulation. Consequently, the 1-D simulation leads to an auto-ignition, whereas the 2-D simulation has a maximum temperature rise of only 59 K. The induced convective flow is determined by the Rayleigh number: Ra =

(β · g · L3 · (Tcentre − Tw )) (αth · ν)

(5.13)


89

Figure 5.15: Evolution of the heat transfer coefficient and the average temperature in the 1-D and 2-D simulation for a 60 mol% methane-air mixture at an initial temperature of 713 K and an initial pressure of 0.5 MPa.

Figure 5.16: Comparison of the temperature history of the 1-D simulation (a) and the 2-D simulation (b) for a 60 mol% methane-air mixture at an initial temperature of 713 K and an initial pressure of 0.5 MPa.

90


Time [s] 5 10 15 20 30

Tcentre - Twall [K] 3.5 10−3 5.1 10−2 3.8 10−1 1.5 5.3

Rayleigh Number [-] 2.3 102 3.3 103 2.5 104 9.4 104 3.4 105

Table 5.3: Evolution of the Rayleigh number of the 2-D simulation for a 60 mol% methane/air mixture at an initial temperature of 713 K and an initial pressure of 0.4 MPa.

where β is the coefficient of thermal expansion, L is the characteristic length (radius) of the vessel, αth is the thermal diffusivity and ν is the kinematic viscosity. The natural convection becomes important when the Rayleigh number rises above 500 or 1.7 103 as stated by Campbell et al. (2007) and Bejan (2004), respectively. It can be seen from Table 5.3 that the Rayleigh number rises above 103 at 10 seconds. At 20 seconds the temperature rise is 1.5 K and the Rayleigh number is 105 . This means that natural convection is important. Figure 5.17 shows the temperature evolution along the vertical axis for a 2-D simulation with an initial pressure of 0.6 MPa and an initial temperature of 713 K. The temperature profiles are scaled to their respective maximum temperatures, which can be seen on top of the separate figures of figure 5.17. At 10 seconds the temperature profile is symmetrical. From 20 seconds onwards the maximum temperature shifts to the top of the vessel due to natural convection. The increase of the maximum temperature is accompanied by a decrease of the area of the hot zone. At 60 seconds the maximum temperature is 200 K higher than the initial temperature and the simulation is classified as an auto-ignition. Because the maximum temperature is only present at a small area at the top of the vessel, it is important for the experimental determination of the auto-ignition limit to measure the temperature at the top of the vessel. Figure 5.18 presents the velocity profiles corresponding to the 2-D simulation of figure 5.17. It can be seen that the maximum velocity increases with time. Initially the velocities caused by the buoyant flow are very small because the temperature rise is very small. From 20 seconds onwards the velocities become significantly larger and rise to values of almost 10 cm/s. Furthermore, a recirculation zone arises and shifts to the bottom of the vessel. During the auto-ignition the maximum velocities occur mainly at the wall of the vessel. Although the two-dimensional auto-ignition limit shows an excellent agreement with the experimental data, it is also important to compare the temperature and pressure histories of the simulations with the experimental measurements in order to evaluate the validity of the two-dimensional model. The temperature and pressure histories of an experiment and a simulation with an initial temperature of 683 K and an initial pressure of 1.4 MPa are presented in figure 5.19. At first sight the simulation shows many similarities with the experimental data. Initially the temperature and pressure rise are small. After


91

Figure 5.17: History of the temperature profile along the vertical axis of a 2-D simulation of a 60 mol% methane-air mixture at an initial temperature of 713 K and an initial pressure of 0.6 MPa.

3.5 cm/s

6.9 cm/s

7.9 cm/s

9.0 cm/s

10 s

20 s

30 s

40 s

50 s

Vertical axis

0.1 cm/s

Figure 5.18: Velocity profiles of a 2-D simulation of a 60 mol% methane-air mixture at an initial temperature of 713 K and an initial pressure of 0.6 MPa.

some time, the temperature at the top of the vessel increases sharply. This time is called the auto-ignition delay time. Subsequently, the elevated temperature, i.e. the temperature 6 cm above the centre, and the central temperature increases. The temperature rises are accompanied by a pressure rise. The maximum temperature of the measurements is similar to the maximum temperature of the simulation. There are nevertheless some differences between the simulation and the experimental measurements. The ignition delay time of the experiment is 110 s, while in the simulation the delay time is only 50 s. The measured temperature at the top of the vessel has a very sharp increase after 110 s, whereas the temperature rise of the simulation is smoother. For the experiment the elevated thermocouple has a sharp temperature increase 1 second after the temperature increase at the top of the vessel. In the simulation this delay time is about 5 seconds. Consequently, the gas mixture can cool down more rapidly and the central temperature only increases to 910 K. As a result, the pressure rise of the simulation is smaller than the measured pressure rise. Despite similarities between the simulation and the experiment, there is still need to refine the reaction mechanism by adding more reaction steps or including wall interactions in order to simulate more accurately the auto-ignition process.

92


Experiment at 683 K and 1.4 MPa (60 mol% methane in air) 2.5 Top Temp Elevated Temp

2

Central Temp Pressure

1.5

1000

1 800

Pressure [MPa]

Temperature [K]

1200

0.5

600 100

105

110

0 120

115

Time [s]

Simulation at 683 K and 1.4 MPa (60 mol% methane in air)

1200

1.5

1000 1.0

800

Pressure [MPa]

Temperature [K]

2.0

Top Temp Elevated Temp Central Temp Pressure

0.5

600

0.0 0

10

20

30

40

50

60

70

80

Time [s]

Figure 5.19: Comparison of the pressure and the temperature histories of an experiment and a simulation with an initial pressure of 1.4 MPa and an initial temperature of 683 K.

5.3 Numerical results of propane/air mixtures

Model 0-D 1-D 2-D 2-D

Reaction Mechanism full BGC full BGC full BGC reduced BGC

Simulation time 600 s 100 s 100 s 100 s

93

Calculation time < 1 min 2h 10 h 2.5 h

Table 5.4: Calculation times of simulations.

5.2.4

Discussion

The results of this study have shown that the coupling of computational fluid dynamics with detailed chemical kinetics is very promising for the modelling of the auto-ignition limits of gas mixtures. The accurate calculation of the autoignition limits of gas mixtures occurring in industrial installations at elevated pressures and temperatures is, however, impeded by a number of factors. First there is a need for reaction mechanisms that are capable to accurately describe the oxidation kinetics in the low temperature region, in which the auto-ignition process occurs. Second, there is a need for accurate and detailed experimental data, preferably obtained in a spherical or an upright cylindrical test vessel since this enables the use of a 2-D model. Third, the calculation time increases significantly with the dimension of the model as can be seen in Table 5.4, which represents the calculation times on an Intel Core 2CPU 2.66 GHz system with 4 GB of memory. The present computational capabilities restrict the calculations to relatively simple reaction mechanisms in combination with a 2-D model.

5.3

Numerical results of propane/air mixtures

The numerical study of the auto-ignition of propane/air mixtures was limited to a comparison of the auto-ignition limits calculated with the 0-D model. As can be seen from table 5.2 in section 5.1.3 the simplest chemical reaction scheme (Westbrook, 1984) consists of 36 species and 168 reactions. These mechanisms would require very long calculation times if they are included into a 1-D or 2-D model. Figure 5.20 presents the 0-D auto-ignition limits predicted by the different reaction schemes. The reaction mechanisms can be divided into two groups. The first five overestimate the auto-ignition temperature. For these reaction mechanisms the explosion criterion applied was a temperature rise of 50 K. At the auto-ignition temperature of 572 K their respective ignition delay times were 18000 s, 10000 s, 5000 s, 13500 s and 23000 s. The explosion criterion with the experiments was a combined temperature rise (> 50 K) and ignition delay time criterion (< 900 s). The model with the Exgas-alkanes kinetics also uses this criterion. Nevertheless this mechanism overrates the auto-ignition risk compared with the experimental data. It can be concluded that there is still a need for reaction mechanisms that are capable to describe accurately the oxidation kinetics in the low temperature region before the reaction mechanisms can be applied in more comprehensive heat transfer models.

94


3.5

Exgas-Alkanes Experiments Koert&Pitz Delaware Princeton Westbrook SanDiego

3


2.5

2

1.5

1

0.5

0 450

500

550

600

650

700

Temperature [K]

Figure 5.20: Numerical modelling of auto-ignition limit of a 40 mol% propane-air mixture, compared with the experimental data using the 0-D model.

Chapter 6

Influence of the vessel size on the auto-ignition temperature of combustible gas-air mixtures Young love is a flame; very pretty, often very hot and fierce, but still only light and flickering. The love of the older and disciplined heart is as coals, deep burning, unquenchable. Henry Ward Beecher, American clergyman and author (1813 – 1887)

T he experimental determination of the AIT is characterised by the small volume of the test vessel. It is typical to use test vessels with a volume less

than 1 litre (see Section 2.2). Auto ignition is a thermo-chemical process in which heat is generated by the combustion reaction. The heat is absorbed by the gas and also transferred to the vessel walls. It is obvious from this that the size and shape of the test vessel must have an impact on the onset of ignition. The question should be put therefore whether these data are relevant for large vessel volumes as is often the case under process conditions. This chapter describes the modelling of the effect of vessel size on the auto ignition temperature (AIT). This is an application of the two dimensional model which is described extensively in the previous chapter. This model takes the natural convection inside the vessel into account and is used to determine the AIT for spherical vessels from 10−3 to 1 m3 . First an overview is given of the models for the volume dependency of the auto-ignition temperature. Thereafter the results obtained with these models in spherical vessels are presented. Finally the auto-ignition temperatures in cylindrical vessels are compared to those in

95

96

Chapter 6 Influence of the vessel size on the AIT

spherical ones.

6.1

Models for the volume dependency of the auto-ignition temperature

In principle recourse can be taken to two theoretical models that describe the phenomena occurring during auto-ignition. The first model is the one developed by Semenov, see section 2.3.2. It considers the gas mixture to behave as a point heat source. The heat is transferred to the vessel walls by means of convection. The combustion reaction is assumed to be a first order step reaction. For spherical vessels this model results in the following relationship between the critical pressure Pc and the gas temperature T at auto-ignition (see equation 2.41): EA C Pc + ln( √ ) (6.1) ln( ) = T0 2RT0 D with EA the activation energy, R the universal gas constant, D the diameter of the vessel and C a constant which is independent of the volume but depends on the convective heat transfer coefficient between the vessel wall and the gas mixture. The second model comes from Frank-Kamenetskii (see Section 2.3.3), who studied the heat transfer in the gas mixture considering heat conduction through the mixture to the (spherical) vessel wall assuming rotational symmetry and again simple Arrhenius type reaction kinetics. He found that at auto ignition conditions the Frank-Kamenetskii parameter is equal to: δ=

Q EA 2 −E A r Ze RTw ≤ δcrit = 3.32 λ RTw2

(6.2)

in which r is the radius of the vessel, Q is the volumetric heat of reaction, λ is thermal conductivity and δcrit is the critical parameter which depends on geometry and is equal to 3.32 for spherical vessels. By comparison of equation 6.1 and 6.2, it can be seen that the two theoretical models have a different volume dependency of the auto-ignition temperature. Beerbower (Coffee, 1980) developed the following empirical correlation for the AIT T2 at volume V2 as a function of the AIT T1 at V1 : T2 =

T1 − 75 T1 − 75 · log(V2 ) + [75 − ] log(V1 ) − 12 log(V1 ) − 12

(6.3)

where the temperatures are expressed in degrees Celsius and the volumes in dm3 . This correlation was obtained by the analysis of the experimentally determined auto-ignition temperatures in different volumes for benzene, acetone, methanol, pentane, etc. It was observed that the auto-ignition temperature decreases linearly with the logarithm of the volume. Equation 6.3 expresses that the auto-ignition temperatures for the different mixtures coincide at a volume of 1012 dm3 at a value of 75 ◦ C. The Beerbower correlation can only

6.2 Model evaluations for spherical vessels

97

be applied to obtain an auto-ignition temperature of a gas mixture at a certain volume if the auto-ignition temperature of that mixture is known at another volume. Furthermore the Beerbower correlation is not validated for the volume dependency of the auto-ignition temperature at elevated pressures. The Semenov model requires the activation energy to be known. An alternative method consists of analysing the detailed combustion reaction kinetics, to determine the rate equations for all of the radicals formed during the reaction and to combine the radical reactions into reaction paths. The 0-D model, which is extensively described in section 5.1 of the previous chapter, is different from the Semenov model because this model uses a full kinetic mechanism instead of one simple Arrhenius reaction. The reaction mechanism is a methane oxidation of the British Gas Corporation (Reid et al., 1984), which resulted in accurate predictions of the auto-ignition limits in closed spherical vessels, as can be seen in chapter 5. It is clear that because of the combustion reaction and the heat transfer with the vessel wall temperature differences will occur giving rise to buoyancy driven flows of the mixture. Such flows will have an impact upon the heat transfer with the vessel walls (convective effect) and thus on the heat transfer coefficient occurring in the Semenov model. A two-dimensional CFD flow model is applied in order to take this phenomenon into account. This model, called the 2-D model, also incorporates the detailed chemical kinetics of the 0-D model and is described in more detail in section 5.1.

6.2

Model evaluations for spherical vessels

The different models are evaluated for a 60 mol% methane in air mixture. The theoretical models, such as the Semenov and the Frank-Kamenetskii model, require the overall activation energy of the combustion reaction. At first the results of the zero-dimensional model will be presented, which will be used to determine the value of the overall activation energy. Up to now the autoignition limits were calculated in a closed vessel with a volume of 8 litres. In order to retrieve the volume dependency of the auto-ignition temperature five different volumes are considered. These spherical vessels have a volume of 1, 8, 64, 512 and 4096 litres. The auto-ignition temperatures of a 60 mol% methane/air mixture and different volumes calculated with the zero-dimensional model are presented in figure 6.1. It can be seen that for a pressure of 0.1 MPa and a volume below 10 litres, there is a sharp increase of the auto-ignition temperature. For higher pressures the decrease of the auto-ignition temperature is linear as a function of the volume. The slope of the curves slightly decreases for increasing pressure. The results of the 0-D model and the experimental autoignition limits obtained in this study are presented in a Semenov plot in figure 6.2. The overall activation energy can be retrieved from the slope of curves, see equation 6.1. It can be seen that the slope of the experimental data is in good agreement with the slope of limits obtained with the zero-dimensional model.

98


Auto-ignition Temperature [K]

1100 Limit @ 0.1 MPa Limit @ 0.3 MPa Limit @ 0.5 MPa Limit @ 1 MPa Limit @ 2 MPa Limit @ 5 MPa Limit @ 10 MPa

1000

900

800

700

600

500 1

10

100

1000

10000

Volume [dm³]

Figure 6.1: The volume dependency of the auto-ignition temperature calculated with the zero-dimensional model.

The average activation energy of the experiments and of the zero-dimensional calculations for a volume of 8 litres is found to be 160 kJ/mol. The activation energy of rich methane/air mixtures was also measured by Melvin (1966), who found an activation energy for a 60 mol% methane/air mixture of respectively 170 KJ/mol and 183 kJ/mol depending if the activation energy was calculated from measurements of the rate of temperature rise or measurements of the ignition delay. These activation energies are in good agreement with the value of 160 kJ/mol of this study, in particular if they are compared with the value of 339 kJ/mol for the activation energy in the low pressure explosions of methane and oxygen (Melvin, 1966). Consequently the value of 160 kJ/mol is used in the Semenov model. Figure 6.3 compares the results of the zero-dimensional model with the autoignition temperatures obtained with the Semenov correlation. At a pressure of 0.5 MPa, the limit obtained with the zero-dimensional model is similar to the auto-ignition limit according to the Semenov theory. At 0.1 MPa there is a significant difference between both limits for the small volumes. At high volumes both limits have a similar volume dependency. For high pressures the limits obtained with the Semenov correlation show a larger volume dependency than the limit obtained with the 0-D model. The differences between both limits can be explained through the fact that the Semenov theory only includes one reaction with one activation energy. In the 0-D model a full chemical kinetics mechanism is applied. The average global activation energy clearly depends on the mixture pressure. From figure 6.2 it can be seen that the slope of the auto-ignition limit significantly changes for the small volumes and high temperatures. This explains the large differences at a pressure of 0.1 MPa. Figure 6.4 presents the different auto-ignition limits obtained with the

99

6.2 Model evaluations for spherical vessels

10

9

ln (p/T)

8 1 litre 200K

7

8 litre 200K 64 litre 200K

6

512 litre 200K 4096 litre 200K

5

Experimental data

4 0.001

0.0011 0.0012 0.0013 0.0014 0.0015 0.0016 0.0017 0.0018 0.0019

0.002

1/T [1/K]

Figure 6.2: Semenov plot of the experimental AIT and the AIT calculated with the zero-dimensional model.


1100 0-D limit @ 0.1 MPa Semenov limit @ 0.1 MPa 0-D limit @ 0.5 MPa Semenov limit @ 0.5 MPa 0-D limit @ 1 MPa Semenov limit @ 1 MPa 0-D limit @ 5 MPa Semenov limit @ 5 MPa

1000

900

800

700

600

500 1

10

100

1000

10000

Volume [dm³]

Figure 6.3: Comparison of the calculated auto-ignition temperatures of the zerodimensional model with the results of the Semenov model.


100


900

Semenov @ 0.1 MPa

Semenov @ 1 MPa

Semenov @ 5 MPa

Frank-Kam. @ 0.1 MPa

Frank-Kam. @ 1 MPa

Frank-Kam. @ 5 MPa

Beerbower @ 0.1 MPa

Beerbower @ 1 MPa

Beerbower @ 5 MPa

800

700

600

500 1

10

100

1000

10000

Volume [dm³]

Figure 6.4: Comparison of the calculated auto-ignition temperatures using the Semenov and the Frank-Kamenetskii model and the Beerbower correlation.

Frank-Kamenetskii and the Beerbower correlation for different pressures. The auto-ignition limits of the Semenov model for a volume of 8 litres were used for the application of the Frank-Kamenetskii theory and the Beerbower correlation. Therefore the Semenov limits coincides with the limits at a volume of 8 litres for both these models. The limit according to the Frank-Kamenetskii theory decreases significantly more than the Semenov limit when the vessel volume is increased. From equations 6.1 and 6.2 it follows that the Semenov AIT at a volume of 512 litres is similar to the Frank-Kamenetskii AIT at a volume of 64 litres. The auto-ignition limits according to the Beerbower correlation, which has no theoretical underpinning, lies between the limits determined with the Semenov and Frank-Kamenetskii theory. The previous models require the knowledge of the activation energy, the heat transfer coefficient or experimentally determined auto-ignition limits. An alternative approach is the 2-D CFD model which includes the full kinetics mechanism and incorporates natural convection. It is expected that the natural convection will play an important role in the determination of the auto-ignition temperature for large volumes. In figure 6.5 the 2-D model results are shown together with the results of the Semenov models for an initial pressure of 0.5 MPa, 1 MPa and 5 MPa. It can be seen that the auto-ignition limits of the 2-D models lie higher in comparison with the Semenov limits. This can be explained by the increasing heat loss due to the natural convection that is taken into account in the 2-D model which hampers the auto-ignition. At a pressure of 0.5 MPa it can be seen that the limit obtained with the 2-D model has a slightly higher decrease with increasing volume in comparison with the Semenov model. This effect disappears at a pressure of 5 MPa at which the Semenov limit and the 2-D model shows an identical decrease. By


6.3 Model evaluations for vertical cylindrical vessels

800

Semenov @ 0.5 MPa

Semenov @ 1 MPa

Semenov @ 5 MPa

2-D model @ 0.5 MPa

2-D model @ 1 MPa

2-D model @ 5 MPa

101

700

600

500 1

10

100

1000

10000

Volume [dm³]

Figure 6.5: Comparison of the calculated auto-ignition temperatures using the Semenov and the 2-D model.

comparison of figures 6.4 and 6.5 it can be concluded that the 2-D model shows the auto-ignition temperature to decrease less rapidly with increasing volume in comparison with the Frank-Kamenetskii and the Beerbower model.

6.3

Model evaluations for vertical cylindrical vessels

In process installations the reactors are mostly cylindrical vessels instead of spheres because of their cheapness. Therefore it is important to know how the auto-ignition temperature behaves in cylindrical vessels with increasing volume. The question should be put how accurate are the auto-ignition temperatures obtained with the Semenov model and the Beerbower correlation for changing cylindrical volumes because these models are not valid for cylindrical geometries. The Frank-Kamenetskii model was also derived for cylindrical geometries. The critical Frank-Kamenetskii parameter changes to 2.00 for infinite cylinders instead of 3.32 for spheres and the length used in the parameter formula is equal to the radius of the cylinder, as can be seen in section 2.3.3. It follows from the Frank-Kamenetskii theory that the auto-ignition temperature inside infinite cylinders depends solely on the radius of the cylinder. It is not possible to include the effect of finite cylinders on the auto-ignition temperature according to the Frank-Kamenetskii model. Since the existing theoretical models cannot supply a satisfactory answer to the question of the volume dependency of the AIT in cylindrical geometries, the auto-ignition temperatures are calculated by means of the 2-D CFD-kinetics model. At first a cylinder with a volume of 8 litres and a diameter/height ratio

102



900

800

Sphere @ 0.5 MPa

Cylinder @ 0.5 MPa

Sphere @ 1 MPa

Cylinder @ 1 MPa

Sphere @ 5 MPa

Cylinder @ 5 MPa

700

600

500 1

10

100

1000

Volume [dm³]

Figure 6.6: Comparison of the 2-D auto-ignition temperatures for spheres and vertical cylinders.

equal to 1 was modelled. A cylinder has similar to a sphere an axisymmetry axis according to direction of the gravity force. Consequently the grid consists of a 2-D rectangle. The grid size and the time step independence are checked by varying their values until no influence on the result was observed. Next to the 8 litres vessel similar calculations are performed with increasing cylinder volume. The surface area of the bottom and the top of the cylinder is not altered; the volume of the cylinder therefore is directly proportional to the height of the cylinder. The results are shown in figure 6.6. The auto-ignition limits at a volume of 8 litres are in excellent agreement with the ones obtained for the spherical vessel. At a pressure of 0.5 MPa the auto-ignition limit of the cylinder is in good agreement with the limit obtained for the sphere. At higher pressures the auto-ignition temperature for cylindrical vessels decreases less for increasing volume than the limit for spherical vessels. At high pressures and at large volumes, the auto-ignition temperature shows almost no volume dependency. This is because of the higher buoyancy creating a high temperature zone at the top of the cylinder, see figure 6.7. Ignition is governed by the heat production and heat loss at the top of the cylinder. Because the size of the top surface of the cylinder was not changed for increasing cylinder volume, the auto-ignition temperature does not change. At elevated pressures and for a height/diameter ratio of more than eight the AIT is only dependent on the radius of the vessel, as was predicted by the Frank-Kamenetskii model for infinite cylinders.

6.4

Conclusions

It is found that the existing models to predict the volume dependence of the auto ignition temperature of gas mixtures require the knowledge of parameters such as activations energies, heat transfer coefficients (Semenov, Frank-

103

6.4 Conclusions

20s

40s

60s

70s

80s

90s

100s

780 K

730 K

680 K Figure 6.7: Temperature evolution of a 2-D simulation of a 60 mol% methane/air mixture at 680 K and 1.0 MPa in a vertical cylinder with a volume of 64 litres.

Kamenetskii) or experimentally determined auto-ignition conditions (Beerbower). An alternative approach not needing these a priori data is possible but requires detailed chemical kinetics to describe the combustion reactions and the fluid flow. Such a method has been developed for methane-air mixtures and can be applied to spherical as well as cylindrical vessels.

104


Chapter 7

Conclusions and recommendations 7.1

Conclusions

T he aim of this study is to investigate experimentally and numerically the influence of process conditions on the auto-ignition temperature (AIT) of different alkane mixtures. Although many AIT values of hydrocarbon-air mixtures can be found in literature, these values are generally determined according to the standard test methods in small vessels and at atmospheric pressures. Experimental auto-ignition data of hydrocarbon-air mixtures at elevated pressures are scarce. Since many industrial processes operate at high pressures and high temperatures, detailed knowledge about the auto-ignition temperatures at these conditions is essential for the safe and economic operation of those processes. The aim of this study is to help fill this hiatus. This thesis encompasses first a theoretical part, in which an overview of parameters and factors that influence the auto-ignition temperature and different auto-ignition theories are presented. In the experimental part a large set of consistent auto-ignition data is generated for methane, propane and butane mixtures which can be of direct use for industrial applications or which can be used for the validation of the numerical models. The last part of this thesis consists of the numerical simulation of the auto-ignition process.

Theoretical and literature studies Although an auto-ignition process can be represented simply as a balance between the heat production from the chemical reactions and the heat loss to the surrounding walls, the literature study revealed the complexity of the autoignition phenomenon. The auto-ignition temperature is not constant for a certain combustible gas mixture, but is influenced by many factors and parameters. In chapter 2 a broad overview of these influences are presented. Because

105

106

Chapter 7 Conclusions and recommendations

no standard method exists for the determination of the auto-ignition temperature at elevated pressures a new standard procedure was developed in this thesis. Therefore the existing standards for the determination of the AIT are compared and their shortcomings were revealed. The last section of chapter 2 describes three auto-ignition theories, which will be applied in the different parts of this study.

Experimental study The experimental study consists of the determination of the auto-ignition limits of propane and butane mixtures at elevated pressures up to 3 MPa for a wide range of concentrations inside a closed vessel of 8 l (Chapter 4). A standard operating procedure is developed. It is shown that the auto-ignition temperatures decrease significantly with increasing pressure. The auto-ignition temperature of a 40 mol% propane/air mixture is 573 K at atmospheric pressure and decreases to 523 K at a pressure of 1.5 MPa. The AIT’s of n-butane/air mixtures are lower compared to the AIT’s of propane. For example, the AIT of a 50 mol% n-butane/air mixture is 548 K at atmospheric pressure and decreases to 503 K at a pressure of 1.7 MPa. The AIT’s of i-butane are comparable to the AIT’s of propane. The AIT of a 50 mol% i-butane/air mixture is 573 K at atmospheric pressure and decreases to 523 K at a pressure of 1.3 MPa. These AIT’s are significantly lower than the AIT’s determined by the standard methods which are 743 K, 733 K and 638 K for propane, i-butane and n-butane respectively. It is also found that the combustible concentration most sensitive to auto-ignition depends on the initial pressure. The auto-ignition pressures (AIP) of two propane/butane (LPG) mixtures are determined and compared to the auto-ignition limits of their respective components. The minimum AIP at 523 K are 0.39 MPa and 0.32 MPa for the 50/50 propane/n-butane mixture and the 40/30/30 propane/n-butane/i-butane mixture respectively. These AIP’s are in good agreement with the minimum AIP (0.30 MPa) of n-butane at 523 K, which is the component with the lowest AIP. The upper flammability limits (UFL) of propane and butane mixtures show a linear increase with increasing initial temperatures. At high temperature a deviation from the linear dependence of the UFL’s was found by Van den Schoor (2007). By comparison of the auto-ignition limits with the upper flammability limits of propane and n-butane at elevated pressures it is concluded that the deviating UFL’s lie inside or very close to the auto-ignition range (Section 4.4). The last part of the experimental study consisted of the determination of the auto-ignition limits of methane/air mixtures at elevated pressures and for different concentrations. Methane is the smallest alkane and has the highest auto-ignition temperature of the alkanes. The AIT of a 60 mol% methane in air mixture is 713 K at a pressure of 0.9 MPa and decreases to 653 K at a pressure of 2.9 MPa. The experimental results were initially strongly affected by the remaining reaction products and the rust formation inside the explosion vessel. Therefore the standard operating has been adapted and this resulted in a significantly improvement of the repeatability of the auto-ignition data.

7.2 Recommendations for further research

107

The temperature measurements at different locations inside the explosion vessel make it possible to describe qualitatively the auto-ignition process at elevated pressures.

Numerical study At the beginning of this research it was a major challenge to make a coupling of the detailed chemistry with computational fluid dynamics in order to simulate the auto-ignition process. It soon became clear that the coupling of detailed chemical kinetics with hundreds of reactions and a two or three dimensional fluid calculation is not feasible. Therefore certain simplifications are needed. The numerical study mainly focuses on the modelling of the auto-ignition of methane/air mixtures. Since methane is the smallest hydrocarbon, the existing reaction mechanisms of methane are smaller compared to the mechanisms of higher alkanes. First a zero-dimensional approach is adopted in order to compare the different reaction mechanisms. A methane reaction mechanism of the British Gas Corporation shows the best agreement with the experimental results. Subsequently, to take thermal and mass diffusion and the natural convection inside the vessel into account a two-dimensional model is built including the kinetic mechanism. A CFD-model is used to compute the heat transfer and the buoyant flows inside the vessel. The coupling of the reaction mechanism to this model results in an accurate prediction of the auto-ignition conditions of methane/air mixtures at elevated pressures inside a closed vessel. This model is also used to investigate the volume dependency of the autoignition temperature for both spherical and cylindrical vessels. The results are in good agreement with empirical and theoretical correlations. This 2-D model can also be applied for the auto-ignition modelling at real process conditions. These are, for example, the ignition at hot surfaces, the auto-ignition in specific volumes and the auto-ignition in forced flows. The 0-D auto-ignition modelling of propane/air mixtures reveals that there is still need for accurate reaction mechanisms validated for the auto-ignition in the low temperature region before the reaction mechanisms can be applied in more comprehensive heat transfer models.

7.2

Recommendations for further research

This study has hopefully contributed to a safer and more economic operation of industrial processes. The experimental part consists of a substantial enlargement of the available auto-ignition data of low alkane/air mixtures at elevated pressures. Additionally, the numerical study pioneers the coupling of detailed chemical kinetics with CFD calculations in order to model the auto-ignition inside closed vessels. Although this study has taken next steps both on experimental and numerical level, further research is necessary. In the following paragraphs some recommendations for further research on both experimental and numerical level are presented.

108


Experimental work • The experimental part of this study consisted of experiments with methane, propane and butane mixtures. To complete the homologous series of the lower alkanes, auto-ignition experiments with ethane mixtures should be performed. Experimental auto-ignition data of higher alkanes or alkenes at elevated pressures is essential for the validation of the chemical kinetics mechanisms. • The oxidant used in this work was compressed dry air. Since many chemical processes are operating in oxygen rich or oxygen poor environments, the influence of the oxidiser should be investigated. Therefore auto-ignition experiments with oxygen-enriched and oxygen-poor air or with other oxidiser such as nitrous oxide should be performed. These data could improve the applicability of the kinetic mechanisms. • Many other influences on the auto-ignition temperature at elevated pressures still can be investigated experimentally. These are, for example, the volume dependency, the material effect and the influence of turbulence. • The experiments of this study were conducted in a homogenously heated explosion vessel. In many industrial situations the heat source that causes auto-ignition is not homogenous, but is a local hot spot. This can be a hot tube or a hot burner stone. Therefore the influence of the hot surface area on the ignition temperature should be investigated experimentally.

Numerical simulation • The numerical simulations of this study have revealed some shortcomings of the chemical kinetics modelling at elevated pressures. First few reaction mechanisms are validated for elevated pressures. Only a few hydrocarbon reaction mechanisms exist for high pressures, but these are mainly validated by means of shock tube experiments with very short induction times. Therefore these reaction mechanisms are not appropriate for the modelling of auto-ignition with long inductions times. Further research is necessary to improve these reaction mechanisms for the experimental conditions. The experimental data of this thesis could serve for the validation of these reaction mechanisms. • This study developed a CFD-kinetics model for the auto-ignition of methane inside closed vessels at elevated pressures. This model could have many applications such as the auto-ignition modelling in different volumes and with changing flow conditions or the modelling of hot surface ignitions. • The numerical model described the gaseous reactions that take place during the auto-ignition. It was seen in section 2.1 that the material has an influence on the auto-ignition temperatures. Therefore, surface

7.2 Recommendations for further research

109

reactions should be included in order to predict the material effect on the auto-ignition temperature.

110


Appendices

111

Appendix A

Test results D uring this study a large number of experiments were performed in the 8 l spherical test vessel. In this appendix the auto-ignition experiments are summarised.

Propane: First series fuel [mol%]

T0 [K]

Tmax [K]

∆T [K]

P0 [MPa]

Pmax [MPa]

Press. ratio[-]

IDT [s]

Explo?

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 60 60 60

573 573 573 573 573 573 573 573 573 573 573 573 573 573 573 573 573 573 573 573 573

577 577 578 577 1195 1156 1110 1111 1095 1111 1113 1107 1123 1075 1063 1110 573 573 703 683 627

4 4 5 4 622 583 537 538 522 538 540 534 550 502 490 537 0 0 130 110 54

0.775 0.810 1.010 0.850 1.440 1.250 1.120 1.060 1.020 1.030 1.000 0.970 0.950 0.920 0.850 0.850 0.820 0.820 0.825 0.580 0.320

0.775 0.810 1.010 0.850 5.080 5.080 4.830 4.550 4.340 4.480 4.190 4.080 3.990 3.850 3.480 3.510 0.820 0.820 1.240 0.840 0.393

1.00 1.00 1.00 1.00 3.53 4.06 4.31 4.29 4.25 4.35 4.19 4.21 4.20 4.18 4.09 4.13 1.00 1.00 1.50 1.45 1.23

x x x x 570 400 372 425 790 575 880 700 757 755 770 863 x x 45 60 138

no no no no yes yes yes yes yes yes yes yes yes yes yes yes no no yes yes yes

113

114

Appendix A Test results

60 60 60 50 50 50 50 60 60 60 60 50 50 40 40 40 30 30 30 30 30 30 30 30 40 40 40 40 40 40 40 50 50 50 50 60 60 60 60 60 60 60 60 70 70 70

573 573 573 573 573 573 573 548 548 548 548 548 548 548 548 548 548 548 548 548 548 573 573 573 573 573 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523

628 629 621 653 640 573 620 648 608 599 576 603 548 548 683 548 548 761 751 745 731 673 573 663 641 600 523 523 523 768 768 769 743 523 723 695 702 671 658 633 621 626 523 603 587 581

55 56 48 80 67 0 47 100 60 51 28 55 0 0 135 0 0 213 203 197 183 100 0 90 68 27 0 0 0 245 245 246 220 0 200 172 179 148 135 110 98 103 0 80 64 58

0.280 0.250 0.205 0.280 0.200 0.110 0.156 0.580 0.380 0.345 0.290 0.300 0.253 0.290 0.452 0.402 0.497 0.690 0.640 0.608 0.530 0.203 0.106 0.152 0.154 0.103 0.998 1.520 1.980 2.210 2.145 2.157 1.850 1.590 1.635 2.135 2.105 1.750 1.542 1.330 1.210 1.277 1.235 1.442 1.305 1.190

0.386 0.308 0.246 0.390 0.280 0.110 0.190 0.740 0.445 0.394 0.310 0.348 0.253 0.290 0.708 0.407 0.497 1.522 1.803 1.287 1.062 0.385 0.106 0.247 0.215 0.115 0.998 1.520 1.980 4.160 3.960 3.345 2.741 1.590 2.346 3.060 2.798 2.250 1.932 1.572 1.380 1.493 1.235 1.615 1.440 1.285

1.38 1.23 1.20 1.39 1.40 1.00 1.22 1.28 1.17 1.14 1.07 1.16 1.00 1.00 1.57 1.01 1.00 2.21 2.82 2.12 2.00 1.90 1.00 1.63 1.40 1.12 1.00 1.00 1.00 1.88 1.85 1.55 1.48 1.00 1.43 1.43 1.33 1.29 1.25 1.18 1.14 1.17 1.00 1.12 1.10 1.08

172 204 210 85 150 x 570 220 480 580 850 750 x x 750 x x 720 750 750 890 240 x 140 138 220 x x 732 900 940 390 570 630 740 910 880 535 620 808 1005 870 980 522 580 655

yes yes yes yes yes no yes yes yes yes no yes no no yes no no yes yes yes yes yes no yes yes yes no no no yes yes yes yes no yes yes yes yes yes yes yes yes no yes yes no

115

A.0

70 70 30 30 30 30 30 30 30 30 30 30 40 40 40 40 40 50 50 50 50 50 60 60 60 60

523 523 523 536 536 536 536 536 536 536 536 536 536 536 536 536 536 536 536 536 536 536 536 536 536 536

569 571 523 915 775 790 711 536 536 536 715 719 685 536 536 690 536 652 536 536 536 625 536 636 603 536

46 48 0 379 239 254 175 0 0 0 179 183 149 0 0 154 0 116 0 0 0 89 0 100 67 0

1.120 1.150 2.495 1.105 0.698 0.710 0.405 0.200 0.295 0.336 0.405 0.455 0.445 0.245 0.342 0.453 0.400 0.453 0.255 0.342 0.400 0.455 0.395 0.537 0.410 0.352

1.175 1.218 2.495 2.986 1.692 1.717 0.884 0.200 0.295 0.336 0.840 0.908 0.733 0.245 0.342 0.742 0.400 0.624 0.255 0.342 0.400 0.560 0.395 0.666 0.472 0.352

1.05 1.06 1.00 2.70 2.42 2.42 2.18 1.00 1.00 1.00 2.07 2.00 1.65 1.00 1.00 1.64 1.00 1.38 1.00 1.00 1.00 1.23 1.00 1.24 1.15 1.00

815 753 x 360 515 496 720 x 1010 1030 940 820 640 x x 898 x 540 x x 1010 707 x 476 896 x

no no no yes yes yes yes no no no no yes yes no no yes no yes no no no yes no yes yes no

∆T [K] 263 269 249 243 320 297 254 229 329 240 250 0 10 333 310

P0 [MPa] 0.91 0.78 0.71 0.59 1.44 1.17 0.722 0.57 1.52 0.61 0.588 1.2 1.45 1.6 1.5

Pmax [MPa] 1.648 1.37 1.215 1.004 2.805 2.185 1.234 0.89 2.95 0.985 0.953 1.2 1.46 2.87 2.69

Press. ratio[-] 1.81 1.76 1.71 1.70 1.95 1.87 1.71 1.56 1.94 1.61 1.62 1.00 1.01 1.79 1.79

IDT [s] 460 589 720 908 294 408 810 1380 267 873 706 x 980 797 827

Expl?

Propane: Second series fuel [mol%] 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40

T0 [K] 536 536 536 536 536 536 536 536 536 536 536 523 523 523 523

Tmax [K] 799 805 785 779 856 833 790 765 865 776 786 523 533 856 833

yes yes yes yes yes yes yes no yes yes yes no no yes yes

116


40 40 40 40 40 40 40 40 40 40 40

523 573 573 573 573 548 548 548 548 548 548

829 703 573 728 687 756 747 738 723 548 773

306 130 0 155 114 756 747 738 723 548 773

1.46 0.192 0.1 0.15 0.13 0.51 0.415 0.36 0.3 0.26 0.595

2.596 0.33 0.1 0.24 0.16 0.903 0.72 0.58 0.46 0.26 1.094

1.78 1.72 1.00 1.60 1.23 1.77 1.73 1.61 1.53 1.00 1.84

853 50 x 93 92 303 430 564 765 x 206

yes yes no yes yes yes yes yes yes no yes

∆T [K] 141 140 141 125 105 0 0 227 0 200 240 264 229 234 222 217 210 150 172 139 126 110 0 0 0 379 386 482 634 562

P0 [MPa] 0.430 0.370 0.330 0.280 0.230 0.165 0.200 0.505 0.390 0.430 0.610 0.875 0.700 0.664 0.600 0.560 0.510 1.010 1.210 0.960 0.900 0.790 1.030 1.489 1.635 1.770 1.830 1.950 2.120 2.030

Pmax [MPa] 0.574 0.470 0.413 0.329 0.258 0.165 0.200 0.871 0.390 0.686 1.077 1.643 1.240 1.152 1.012 0.907 0.778 1.233 1.528 1.146 1.055 0.888 1.030 1.489 1.635 3.851 3.966 4.615 5.000 5.000

Press. ratio[-] 1.33 1.27 1.25 1.18 1.12 1.00 1.00 1.72 1.00 1.60 1.77 1.88 1.77 1.73 1.69 1.62 1.53 1.22 1.26 1.19 1.17 1.12 1.00 1.00 1.00 2.18 2.17 2.37 2.36 2.46

IDT [s] 60 246 283 384 298 408 1000 352 409 555 633 783 898 1160 762 559 677 801 1006 1200 1043 1147 522 554

Expl?

Propane: Third series fuel [mol%] 60 60 60 60 60 60 60 40 40 40 40 40 40 40 40 40 40 60 60 60 60 60 30 30 30 30 30 30 30 30

T0 [K] 548 548 548 548 548 548 548 548 548 548 548 536 536 536 536 536 536 523 523 523 523 523 523 523 523 523 523 523 523 523

Tmax [K] 689 688 689 673 653 548 548 775 548 748 788 800 765 770 758 753 746 673 695 662 649 633 523 523 523 902 909 1005 1157 1085

yes yes yes yes yes no no yes no no yes yes yes yes yes yes no yes yes yes yes no no no no yes yes yes yes yes

117

A.0

30 30 30 30 30 40 40 40 40 40

523 523 523 523 523 523 523 523 523 523

909 918 851 817 812 806 797 783 770 754

386 395 328 294 289 283 274 260 247 231

1.780 1.585 1.290 1.030 0.945 1.230 1.140 1.070 0.940 0.855

4.334 3.745 2.916 2.258 2.028 2.420 2.178 1.986 1.670 0.870

2.43 2.36 2.26 2.19 2.15 1.97 1.91 1.86 1.78 1.02

583 636 712 916 1034 650 705 761 876 970

yes yes yes no no yes yes yes yes no

T0 [K] 548 548 548 548 523 523 523 523 523 523 523 523 523 523 523 523 548 548 548 548 548 523 523 523 523 548 548 548 548 548

Tmax [K] 657 628 608 558 523 663 637 609 581 559 551 583 571 548 563 633 646 548 603 579 553 593 635 523 615 638 560 660 633 607

∆T [K] 109 80 60 10 0 140 114 86 58 36 28 60 48 25 40 110 98 0 55 31 5 70 112 0 92 90 12 112 85 59

P0 [MPa] 0.310 0.200 0.160 0.102 0.300 0.800 0.605 0.500 0.420 0.375 0.355 0.485 0.440 0.352 0.405 0.794 0.408 0.112 0.207 0.166 0.110 0.410 0.500 0.360 0.440 0.160 0.095 0.165 0.138 0.100

Pmax [MPa] 0.475 0.279 0.209 0.110 0.300 1.130 0.800 0.622 0.480 0.414 0.391 0.552 0.500 0.380 0.447 1.034 0.565 0.118 0.255 0.185 0.112 0.485 0.672 0.360 0.555 0.255 0.102 0.322 0.232 0.430

Press. ratio[-] 1.53 1.40 1.31 1.08 1.00 1.41 1.32 1.24 1.14 1.10 1.10 1.14 1.14 1.08 1.10 1.30 1.38 1.05 1.23 1.11 1.02 1.18 1.34 1.00 1.26 1.59 1.07 1.95 1.68 4.30

IDT [s] 38 58 66 150 x 228 260 365 554 700 752 420 450 690 530 210 50 x 90 90 x 878 510 x 690 60 x 50 65 90

Expl?

n-Butane fuel [mol%] 50 50 50 50 50 50 50 50 50 50 50 60 60 60 60 60 60 60 60 60 60 40 40 40 40 40 40 30 30 30

yes yes yes no no yes yes yes yes yes yes yes yes no yes yes yes no yes yes no yes yes no yes yes no yes yes yes

118


30 30 20 20 20 20 20 20 20 20 20 20 30 30 30 40 40 40 40 40 40 50 50 50 50 50 50 60 60 60 60 70 70 70 10 10 10 10 10 10 10 10 10 50 50

523 523 523 523 523 523 548 548 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 523 523 523 523 523 523 523 523 523 503 503

648 528 733 728 523 523 705 638 511 1053 1113 511 765 511 768 721 723 715 707 687 678 649 641 633 623 609 511 608 583 555 568 550 558 563 523 523 523 523 523 523 523 523 523 708 698

125 5 210 205 0 0 157 90 0 542 602 0 254 0 257 210 212 204 196 176 167 138 130 122 112 98 0 97 72 44 57 39 47 52 0 0 0 0 0 0 0 0 0 205 195

0.400 0.365 0.485 0.475 0.385 0.443 0.195 0.115 1.490 1.445 1.395 1.400 1.385 1.320 1.350 1.335 1.280 1.205 1.140 1.005 0.950 1.115 1.003 0.925 0.875 0.801 0.765 1.025 0.810 0.710 0.760 0.805 0.870 0.935 0.375 0.555 0.640 0.750 0.875 1.000 1.090 1.200 1.500 2.290 2.002

0.567 0.365 1.186 1.160 0.385 0.443 0.580 0.300 1.490 2.000 4.850 1.400 3.010 1.320 2.880 2.280 2.186 2.024 1.892 1.570 1.445 1.520 1.340 1.230 1.105 0.995 0.765 1.235 0.980 0.770 0.838 0.865 0.955 1.035 0.375 0.555 0.640 0.750 0.875 1.000 1.090 1.200 1.500 3.488 2.938

1.42 1.00 2.45 2.44 1.00 1.00 2.97 2.61 1.00 1.38 3.48 1.00 2.17 1.00 2.13 1.71 1.71 1.68 1.66 1.56 1.52 1.36 1.34 1.33 1.26 1.24 1.00 1.20 1.21 1.08 1.10 1.07 1.10 1.11 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.52 1.47

720 1260 720 740 x 1130 52 64 x 840 160 x 756 1200 847 620 600 665 725 851 910 655 690 788 835 900 990 570 750 890 810 610 540 500 x x x x x x x x 1080 720 810

yes no yes yes no no yes yes no yes yes no yes no yes yes yes yes yes yes no yes yes yes yes yes no yes yes no yes no no yes no no no no no no no no no yes yes

119

A.0

50 50 50 40 40 40 40 40 40 40 40 40 40 60 60 60 60 60 60

503 503 503 503 503 503 503 503 503 503 503 503 503 503 503 503 503 503 503

675 677 669 503 503 768 768 503 503 503 503 768 503 641 623 611 503 611 605

172 174 166 0 0 265 265 0 0 0 0 265 0 138 120 108 0 108 102

1.700 1.730 1.795 2.005 2.488 2.755 2.475 2.445 2.465 2.640 2.750 2.460 2.390 2.240 1.785 1.605 1.405 1.505 1.449

2.360 2.415 2.515 2.005 2.488 4.970 4.416 2.445 2.465 2.640 2.750 4.420 2.390 2.912 2.200 1.926 1.405 1.778 1.725

1.39 1.40 1.40 1.00 1.00 1.80 1.78 1.00 1.00 1.00 1.00 1.80 1.00 1.30 1.23 1.20 1.00 1.18 1.19

920 913 891 1165 960 880 870 935 970 955 x 850 918 598 708 803 960 861 862

no no yes no no yes yes no no no no yes no yes yes yes no yes yes

T0 [K] 573 573 573 548 548 548 523 523 523 573 573 573 548 548 548 523 523 523 523 523 523

Tmax [K] 583 633 618 573 603 593 526 558 578 638 608 633 548 583 613 593 523 523 523 768 768

∆T [K] 10 60 45 25 55 45 3 35 55 65 35 60 0 35 65 70 0 0 0 245 245

P0 [MPa] 0.100 0.205 0.165 0.300 0.395 0.350 0.490 1.380 1.510 0.200 0.110 0.165 0.215 0.305 0.355 1.355 1.300 1.250 1.350 2.000 1.810

Pmax [MPa] 0.107 0.256 0.190 0.320 0.445 0.390 0.490 1.450 1.640 0.260 0.120 0.190 0.215 0.340 0.410 1.500 1.300 1.250 1.350 3.318 2.816

Press. ratio[-] 1.070 1.249 2.364 1.067 1.127 1.114 1.000 1.051 1.086 1.300 1.091 1.152 1.000 1.115 1.155 1.107 1.000 1.000 1.000 1.659 1.556

IDT [s] 120 60 60 330 195 235 x 840 660 80 125 60 x 440 315 890 1200 x x 530 640

Expl?

i-Butane fuel [mol%] 60 60 60 60 60 60 60 60 60 50 50 50 50 50 50 50 50 40 40 40 40

no yes yes no yes yes no no no yes no yes no yes yes yes no no no yes yes

120


40 40 40 40 40 40 40 40 40 40 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 4 4 4 4 4 4 20 20 20 60 60 60 60 30 30 30 30 50 50 40

523 523 523 548 548 548 548 548 573 573 573 573 573 573 523 523 523 523 523 548 548 548 548 548 548 548 548 548 548 548 548 548 548 548 548 536 536 536 536 536 536 536 536 536 536 536

729 713 711 548 548 753 703 548 658 573 573 703 698 703 523 523 768 768 768 548 769 757 741 729 684 548 553 548 548 548 1263 1273 548 851 843 620 569 601 587 768 536 768 756 575 596 536

206 190 188 0 0 205 155 0 85 0 0 130 125 130 0 0 245 245 245 0 221 209 193 181 136 0 5 0 0 0 715 725 0 303 295 84 33 65 51 232 0 232 220 39 60 0

1.642 1.545 1.525 0.365 0.496 0.830 0.605 0.550 0.210 0.170 0.190 0.285 0.238 0.240 1.660 1.810 2.215 2.010 1.855 0.332 0.654 0.605 0.546 0.504 0.412 0.357 0.220 0.293 0.700 1.200 1.360 1.410 0.525 0.630 0.555 0.798 0.590 0.700 0.656 0.998 0.812 0.906 0.848 0.552 0.602 0.651

2.458 2.286 2.213 0.365 0.496 1.320 0.855 0.550 0.310 0.170 0.190 0.555 0.458 0.458 1.660 1.810 4.915 4.170 3.582 0.332 1.290 1.205 0.970 0.893 0.620 0.357 0.220 0.293 0.700 1.200 2.000 7.200 0.525 1.808 1.700 0.948 0.645 0.802 0.735 1.840 0.812 1.602 1.450 0.605 0.688 0.651

1.497 1.480 1.451 1.000 1.000 1.590 1.413 1.000 1.476 1.000 1.000 1.947 1.924 1.908 1.000 1.000 2.219 2.075 1.931 1.000 1.972 1.992 1.777 1.772 1.505 1.000 1.000 1.000 1.000 1.000 1.471 5.106 1.000 2.870 3.063 1.188 1.093 1.146 1.120 1.844 1.000 1.768 1.710 1.096 1.143 1.000

815 885 936 x x 240 830 1125 120 x x 84 60 50 x 1160 550 680 890 x 282 590 557 450 870 x x x x x 960 667 x 299 174 390 660 490 523 710 1105 870 870 890 860 x

yes yes no no no yes yes no yes no no yes yes yes no no yes yes yes no yes yes yes yes yes no no no no no no yes no yes yes yes no yes yes yes no yes yes no yes no

121

A.0

40 40 40 40 20 20 20

536 536 536 536 536 536 536

536 536 703 673 536 768 768

0 0 167 137 0 232 232

0.710 0.760 0.910 0.795 0.985 1.204 1.136

0.710 0.760 1.327 1.296 0.985 3.568 3.692

1.000 1.000 1.458 1.630 1.000 2.963 3.250

x x 730 820 x 850 425

no no yes yes no yes yes

LPG mixture 1: 50 mol% propane and 50 mol% n-butane fuel [mol%] 40 40 40 40 40 40 40 50 50 50 50 60 60 70 70 70 30 30 30 30 30 30 30 40 40 50 50 60 60 60 70 70 40

T0 [K] 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 536 536 536 536 536 536 536 536 536 536 536 536 536 511

Tmax [K] 523 791 741 687 523 668 651 635 523 613 604 583 558 557 574 567 523 770 523 678 536 536 536 536 603 536 592 536 593 575 577 586 511

∆T [K] 0 268 218 164 0 145 128 112 0 90 81 60 35 34 51 44 0 247 0 142 0 0 0 0 67 0 56 0 57 39 41 50 0

P0 [MPa] 0.495 1.205 0.815 0.580 0.440 0.535 0.508 0.545 0.415 0.485 0.455 0.450 0.396 0.452 0.548 0.503 0.515 0.707 0.655 0.303 0.148 0.210 0.252 0.196 0.248 0.200 0.252 0.250 0.352 0.303 0.352 0.403 0.810

Pmax [MPa] 0.495 2.212 1.400 0.870 0.440 0.765 0.697 0.688 0.415 0.593 0.534 0.498 0.432 0.480 0.605 0.551 0.515 1.342 0.655 0.494 0.148 0.210 0.252 0.196 0.296 0.200 0.288 0.250 0.405 0.328 0.384 0.450 0.810

Press. ratio[-] 1.00 1.84 1.72 1.50 1.00 1.43 1.37 1.26 1.00 1.22 1.17 1.11 1.09 1.06 1.10 1.10 1.00 1.90 1.00 1.63 1.00 1.00 1.00 1.00 1.19 1.00 1.14 1.00 1.15 1.08 1.09 1.12 1.00

IDT [s] x 362 470 793 x 890 917 560 922 730 809 624 791 522 403 457 x 888 1050 596 x x 1010 x 640 120 448 x 884 640 386 476 x

Expl? no yes yes yes no yes yes yes no yes yes yes no no yes no no yes no yes no no no no yes no yes no yes no no yes no

122


40 40 40 40 40 40 40 40 50 50 50 50 60 60 60 60 70 70 70 30 30 30 30 30 30 40 40 40 50 50 50 60 60 60 70 70

511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 511 517 517 517 517 517 517 517 517 517 517 517 517 517 517 517 517

511 511 511 799 791 787 783 789 713 709 678 687 628 602 609 615 567 570 555 511 924 871 812 517 517 517 517 710 664 637 517 589 517 581 559 571

0 0 0 288 280 276 272 278 202 198 167 176 117 91 98 104 56 59 44 0 407 354 295 0 0 0 0 193 147 120 0 72 0 64 42 54

1.225 1.414 1.605 2.116 2.025 1.894 1.797 1.840 1.840 1.637 1.344 1.400 1.302 1.016 1.058 1.104 1.110 1.050 1.000 2.588 1.802 1.398 0.994 0.915 0.945 0.700 0.798 0.845 0.870 0.712 0.645 0.650 0.544 0.605 0.646 0.694

1.225 1.414 1.605 3.749 3.424 3.239 3.030 3.113 2.667 2.343 1.812 1.930 1.580 1.178 2.338 2.394 1.221 1.157 1.066 2.588 4.405 3.441 2.240 0.915 0.945 0.700 0.798 1.278 1.170 0.912 0.645 0.732 0.544 0.676 0.703 0.772

1.00 1.00 1.00 1.77 1.69 1.71 1.69 1.69 1.45 1.43 1.35 1.38 1.21 1.16 2.21 2.17 1.10 1.10 1.07 1.00 2.44 2.46 2.25 1.00 1.00 1.00 1.00 1.51 1.34 1.28 1.00 1.13 1.00 1.12 1.09 1.11

x x x 820 850 879 910 880 684 718 925 865 727 916 907 851 810 722 849 x 535 610 775 x x x 950 857 659 852 1020 705 974 854 612 536

no no no yes yes yes yes yes yes yes no yes yes no no yes yes yes no no yes yes yes no no no no yes yes yes no yes no yes no yes

LPG mixture 2: 40 mol% propane, 30 mol% n-butane and 30 mol% i-butane fuel [mol%] 60 60 60 60

T0 [K] 523 523 523 523

Tmax [K] 654 641 618 598

∆T [K] 131 118 95 75

P0 [MPa] 0.627 0.535 0.440 0.370

Pmax [MPa] 0.828 0.680 0.524 0.422

Press. ratio[-] 1.32 1.27 1.19 1.14

IDT [s] 488 578 717 846

Expl? yes yes yes yes

123

A.0

60 60 60 70 70 70 70 50 50 50 50 50 50 50 40 40 40 40 40 40 40 30 30 30 30 30 30 30

523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523

584 554 531 610 591 564 546 680 702 693 683 673 660 641 771 789 785 773 752 723 523 908 913 864 842 810 802 790

61 31 8 87 68 41 23 157 179 170 160 150 137 118 248 266 262 250 229 200 0 385 390 341 319 287 279 267

0.345 0.320 0.255 0.605 0.525 0.440 0.395 0.616 0.765 0.675 0.655 0.605 0.553 0.490 0.905 1.110 1.015 0.900 0.850 0.785 0.580 1.200 1.130 1.060 1.010 0.890 0.855 0.810

0.380 0.337 0.260 0.710 0.581 0.470 0.412 0.860 1.137 0.956 0.914 0.830 0.714 0.602 1.615 2.095 1.880 1.610 1.500 1.340 0.580 2.990 2.860 2.553 2.380 2.038 1.920 1.790

1.10 1.05 1.02 1.17 1.11 1.07 1.04 1.40 1.49 1.42 1.40 1.37 1.29 1.23 1.78 1.89 1.85 1.79 1.76 1.71 1.00 2.49 2.53 2.41 2.36 2.29 2.25 2.21

948 1058 1500 533 709 878 941 798 644 758 813 900 1046 1206 827 606 676 812 869 960 x 746 583 630 666 766 863 931

no no no yes yes no no yes yes yes yes yes no no yes yes yes yes yes no no yes yes yes yes yes yes no

60 60 60 60 60 60 40 40 40 40 40 40 30 30 30 30

523 523 523 523 523 523 523 523 523 523 523 523 523 523 523 523

620 635 631 672 635 629 523 776 802 792 776 765 523 1037 917 883

97 112 108 149 112 106 0 253 279 269 253 242 0 514 394 360

0.610 0.650 0.650 0.930 0.680 0.645 1.090 1.100 1.320 1.240 1.150 1.050 1.130 1.500 1.310 1.170

0.720 0.780 0.780 1.230 0.820 0.770 1.090 2.020 2.570 2.370 2.135 1.860 1.130 4.320 3.390 2.920

1.18 1.20 1.20 1.32 1.21 1.19 1.00 1.84 1.95 1.91 1.86 1.77 1.00 2.88 2.59 2.50

1050 916 912 516 864 922 x 854 651 709 826 1050 x 620 599 659

no no no yes yes no no yes yes yes yes no no yes yes yes

124


Methane fuel [mol%] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 80 80 80 80 80 40 40 40 40 40 40 40 40 40 40 50 50 50 50 50 70 70 70

T0 [K] 653 653 653 653 673 673 673 673 673 673 713 713 713 713 683 683 683 683 683 683 683 683 683 683 683 683 683 683 683 683 683 683 683 683 683 683 683 683 683 683 683

Tmax [K] 663 888 978 893 675 683 873 680 773 823 723 721 946 721 688 913 691 943 833 813 783 843 715 683 683 688 688 691 693 945 963 963 963 943 943 953 933 693 903 873 843

∆T [K] 10 235 325 240 2 10 200 7 100 150 10 8 233 8 5 230 8 260 150 130 100 160 32 0 0 5 5 8 10 262 280 280 280 260 260 270 250 10 220 190 160

P0 [MPa] 2.850 2.960 3.220 2.930 1.550 1.790 2.080 1.775 1.900 1.875 0.860 0.900 1.050 0.930 1.450 1.680 1.540 1.610 1.600 1.480 1.400 1.340 1.280 1.270 1.400 1.460 1.720 1.850 2.030 2.275 2.400 2.510 2.550 2.040 1.920 1.800 1.600 1.520 1.530 1.420 1.275

Pmax [MPa] 2.850 3.596 4.440 3.560 1.550 1.790 2.420 1.780 2.040 2.060 0.860 0.900 1.600 0.925 1.450 2.060 1.540 2.100 1.825 1.650 1.475 1.640 1.310 1.270 1.400 1.460 1.725 1.850 2.030 3.750 3.550 4.100 4.990 3.475 3.110 2.790 2.100 1.520 1.890 1.660 1.425

Press. ratio[-] 1.00 1.21 1.38 1.22 1.00 1.00 1.16 1.00 1.07 1.10 1.00 1.00 1.52 0.99 1.00 1.23 1.00 1.30 1.14 1.11 1.05 1.22 1.02 1.00 1.00 1.00 1.00 1.00 1.00 1.65 1.48 1.63 1.96 1.70 1.62 1.55 1.31 1.00 1.24 1.17 1.12

IDT [s] x 965 600 975 x x 514 x 750 615 x x 62 x x 348 x 204 77 98 115 50 125 x x x x x x 910 1080 928 455 248 350 434 755 x 106 140 183

Expl? no no AIT no no no AIT no no no no no AIT no no AIT no AIT SC SC no SC no no no no no no no no no no AIT AIT AIT AIT no no AIT SC SC

125

A.0

70 40 40

683 713 713

731 963 1093

48 250 380

1.130 1.500 1.200

1.160 3.400 2.300

1.03 2.27 1.92

x 32 131

no AIT AIT

126


Appendix B

Chemical kinetics mechanism I

n the numerical model of this study a chemical kinetic mechanism for the methane oxidation of Reid et al. (1984) is applied. The total set of species and reactions of this mechanism are presented in the subjoined table. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Reactions CH4 +O2 ⇔CH3 +HO2 Reverse Arrhenius coefficient: CH4 +HO2 ⇔CH3 +H2 O2 Reverse Arrhenius coefficient: CH4 +OH→CH3 +H2 O CH4 +H⇔CH3 +H2 Reverse Arrhenius coefficient: CH4 +O→CH3 +OH CH3 +O2 ⇔CH3 O2 Reverse Arrhenius coefficient: CH3 O2 +CH4 →CH3 O2 H+CH3 CH3 O2 +CH2 O→CH3 O2 H+HCO CH3 O2 +HO2 →CH3 O2 H+O2 CH3 O2 +CH3 O2 →CH3 O+CH3 O+O2 CH3 O2 +CH3 →CH3 O+CH3 O CH3 O2 H→CH3 O+OH CH3 +HO2 →CH3 O+OH CH3 O+O2 →CH2 O+HO2 CH3 O+M→CH2 O+H+M CH2 O+O2 →HCO+HO2 CH2 O+HO2 →HCO+H2 O2 CH2 O+OH→HCO+H2 O CH2 O+CH3 →HCO+CH4 CH2 O+H→HCO+H2 CH2 O+O→HCO+OH HCO+O2 →CO+HO2

127

Ai 9.70E+13 1.00E+12 1.50E+13 1.25E+12 1.55E+06 4.22E+14 1.34E+13 2.00E+13 4.00E+11 1.50E+16 3.00E+12 1.00E+12 2.00E+11 2.60E+11 7.00E+12 4.40E+16 2.00E+13 6.30E+10 5.01E+13 2.04E+13 1.00E+12 3.98E+13 1.15E+12 1.97E+13 1.77E+13 1.20E+13

βi 0 0 0 0 2.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Eai 234000 0 95000 17000 10250 62400 57000 37800 0 124500 95000 33500 0 0 0 167000 4500 10900 87900 162800 33500 6000 30200 15400 12800 16600

128

Appendix B Chemical kinetics mechanism

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

HCO+M→CO+H+M CO+HO2 →CO2 +OH CO+OH→CO2 +H H2 O2 +O2 ⇔HO2 +HO2 Reverse Arrhenius coefficient: H2 O2 +M→OH+OH+M H2 O2 +OH→HO2 +H2 O H2 O2 +H→H2 O+OH H2 O2 +H⇔H2 +HO2 Reverse Arrhenius coefficient: H2 O2 +O→OH+HO2 CH3 +CH3 →C2 H6 C2 H6 +HO2 →C2 H5 +H2 O2 C2 H6 +OH→C2 H5 +H2 O C2 H6 +H→C2 H5 +H2 C2 H6 +O→C2 H5 +OH C2 H6 +CH3 →C2 H5 +CH4 C2 H5 +O2 →C2 H4 +HO2 C2 H5 +M→C2 H4 +H+M C2 H4 +OH→CH3 +CH2 O H2 +OH→H2 O+H H2 +O→H+OH HO2 +M⇔O2 +H+M Reverse Arrhenius coefficient: H+O2 →OH+O H+HO2 →H2 +O2 H+HO2 →OH+OH HO2 +OH→H2 O+O2 H2 O+O→OH+OH

1.50E+14 1.00E+14 1.26E+07 1.55E+13 1.50E+12 1.20E+17 4.20E+04 3.80E+14 6.30E+12 1.97E+12 2.80E+13 1.70E+13 6.00E+12 3.60E+12 1.32E+14 3.00E+07 5.00E+14 8.50E+11 1.30E+13 5.00E+12 1.28E+08 1.80E+10 5.20E+15 3.00E+12 1.80E+14 2.80E+13 2.50E+14 5.00E+13 6.80E+13

0 0 1.3 0 0 0 2.5 0 0 0 0 0 0 0 0 2 0 0 0 0 1.5 1 0 0 0 0 0 0 0

61500 96200 -3350 114300 0 190400 -7000 37400 20600 90000 26600 0 81000 6900 39000 21400 90000 16200 171000 0 12300 37200 203000 -4200 70300 0 7900 4200 76800 Ea i

Table B.1: Reaction mechanism rate coefficients in the form ki =Ai · Tβi · exp RT , Units are mol, cm3 , K and J/mol


129

Invloed van procescondities op de zelfontstekingstemperatuur van gasmengsels Inhoudsopgave 1 2 3 4 5

1

Algemene inleiding . . . . . Theoretische achtergrond . . Experimentele studie . . . . Numerieke studie . . . . . . Conclusies en aanbevelingen

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

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. . . . .

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. . . . .

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131 132 133 136 138

Algemene inleiding

Vele chemische processen maken gebruik van brandbare gassen en dampen bij verhoogde drukken en temperaturen. Voor een veilige en optimale werking van deze processen is het belangrijk om de laagst mogelijke temperatuur te kennen waarbij spontane ontsteking kan optreden. In de literatuur zijn de zelfontstekingstemperaturen (AIT’s) van vele chemische stoffen beschikbaar. Deze zijn bepaald volgens gestandaardiseerde methodes in kleine volumes en bij atmosferische druk. Aangezien de zelfontstekingstemperatuur niet constant is maar daalt bij toenemende druk en toenemend volume zijn deze AIT’s niet rechtstreeks toepasbaar voor industriële condities. Het gebrek aan zelfontstekingsdata bij verhoogde drukken en grote volumes en het gebrek aan uitgebreide modellen van het zelfontstekingsproces waren de drijfveren voor deze studie. Deze studie bestaat zowel uit een experimenteel en een numeriek gedeelte. De experimentele studie (Paragraaf 3) bestaat uit het bepalen van de drukafhankelijkheid en de concentratieafhankelijkheid van de zelfontstekingstemperatuur van verschillende alkaan-lucht mengsels. Eveneens worden de zelfontstekingsgrenzen van twee LPG/lucht mengsels bepaald om de invloed van de ver-

131

132


schillende componenten op de zelfontstekingstemperatuur van het mengsel te onderzoeken. In de numerieke studie (Paragraaf 4) wordt een model ontwikkeld voor de simulatie van het thermo-chemische zelfontstekingsproces van methaanlucht mengsels bij verhoogde drukken. Enerzijds gaat het model dieper in op de warmteproductie door de vergelijking van verschillende reactiemechanismen. Anderzijds wordt het warmteverlies gemodelleerd door middel van een 0-, 1en 2-dimensionaal model. Het 2-D model laat toe om de natuurlijke convectie mee in rekening te brengen en de zelfontsteking te simuleren bij reële procescondities. In paragraaf 2 wordt een overzicht gegeven van de verschillende procescondities die de zelfontstekingstemperatuur kunnen beïnvloeden.

2

Theoretische achtergrond

Een zelfontsteking kan beschouwd worden als een gevolg van het onevenwicht tussen de warmteproductie vanwege de chemische reacties en het warmteverlies naar de omgeving. Twee theorieën die de zelfontsteking beschrijven vanuit thermisch oogpunt zijn de theorieën van Semenov (1935) en Frank-Kamenetskii (1955). Een tweede groep van theorieën beschrijven de zelfontsteking vanuit chemisch oogpunt, zoals het chemisch vertakkingsmodel. Deze twee groepen van theorieën vormen de basis voor de numerieke modellen ontwikkeld in deze studie. De zelfontsteking is een zeer complex fenomeen, beïnvloed door vele verschillende factoren. De belangrijke invloedsparameters kunnen opgesplitst worden in drie groepen. Ten eerste zijn er de parameters die afhangen van het mengsel: • Druk. Een verhoging van de druk zorgt voor een grotere stijging van warmteproductie ten opzichte van de toename van het warmteverlies. Daardoor daalt de AIT bij toenemende druk. • Brandstof. De zelfontstekingstemperatuur is sterk afhankelijk van de brandstof. In het algemeen daalt de zelfontstekingstemperatuur daalt bij toenemende ketenlengte en stijgt bij toenemende graad van vertakking bij alkanen. • Concentratie. De concentratie met de laagste zelfontstekingstemperatuur komt meestal niet overeen met de stoichiometrische concentratie, maar de laagste zelfontstekingstemperatuur komt voor bij rijkere mengsels. In deze studie wordt nagegaan wat de gevoeligste concentratie is voor de verschillende alkaan/lucht mengsels bij de verschillende drukken. • Additieven. De toevoeging van componenten met een lagere zelfontstekingstemperatuur zorgt voor een verlaging van de AIT van het gasmengsel. Een onnauwkeurige voorspelling van de AIT van een mengsel is de AIT van de component met de laagste AIT. Sommige additieven kunnen de zelfontsteking bevorderen ondanks dat ze zelf een hogere AIT hebben. Bijvoorbeeld ammoniak kan de AIT van methaan/lucht mengsels verlagen, terwijl ammoniak een hogere AIT heeft dan methaan.

3 Experimentele studie

133

• Oxidator. Meestal wordt lucht aangewend als oxidator. Wanneer zuurstof verrijkte lucht als oxidator gebruikt wordt kan dit de zelfontstekingstemperatuur verlagen. Ten tweede zijn er de apparaatparameters: • Volume. De AIT daalt met toenemend volume van het testvat. Aangezien de meeste industriële processen gebruik maken van grote volumes is onderzoek naar de volumeafhankelijkheid van de AIT heel belangrijk. • Materiaaleffect. Het materiaal van het testvat kan zowel een bevorderend als remmend effect hebben op de zelfontsteking. Hilado en Clark (1972) hebben aangetoond dat de zelfontstekingstemperatuur 30 K kan dalen als er ijzeroxide (roest) wordt toegevoegd aan het testapparaat. • Stroming. Een verhoging van de stroomsnelheid en de turbulentie zorgt voor een grotere warmteafgifte en bemoeilijkt de zelfontsteking. Daardoor stijgt de zelfontstekingstemperatuur. Aangezien de gestandaardiseerde opstellingen gebruik maken van stationaire mengsels geven ze aanleiding tot conservatieve AIT wat betreft de stromingscondities. Ten derde zijn er de methodeparameters, zoals het zelfontstekingscriterium. Meestal wordt een visueel criterium toegepast voor de bepaling van een zelfontsteking. Bij verhoogde druk is een visuele toegang moeilijk te realiseren. Alternatieve methodes zijn temperatuurs- en drukmetingen of de analyse van reactieproducten. Deze thesis focust op het ontwikkelen van een aangepast criterium.

3

Experimentele studie

Experimentele methode De experimentele opstelling voor de bepaling van de zelfontstekingsgrenzen bij verhoogde drukken bestaat uit vier delen: de gasmenginstallatie, het buffervat, het explosievat en de meet- en regelapparatuur, zie figuur 1. Het testmengsel wordt onder hoge druk opgeslagen in het buffervat. Het explosievat heeft een inwendig sferisch volume van 8 liter en is bestand tot explosiedrukken van 400 bar bij een temperatuur van 550 ◦ C. De testprocedure is als volgt. Initieel wordt het explosievat opgewarmd tot de gewenste testtemperatuur. Na het vacuümzuigen wordt het explosievat gevuld met het buffermengsel tot de gewenste begindruk. Het zelfonstekingscriterium is gebaseerd op de temperatuursstijging en de drukstijging van het gasmengsel, zie tabel 2. De ontstekingsuitsteltijd, dit is de tijd na het vullen van het explosievat tot het moment van ontsteking, bedraagt maximaal 15 min. Door het variëren van de initiële druk van de opeenvolgende testen wordt de zelfontstekingsgrens bepaald met een stapgrootte van 0.05 MPa. De zelfontstekingsdrukken zijn gedefinieerd als de hoogste drukken waarbij geen zelfontsteking optreedt.

134


ontspanner

tegendrukregelaar

vloeistofpomp

filter

MFC A

spui

MFC B

spui

mengvat breekplaat

MFC C

debietmeter perslucht

vacuümpomp

verdamper PV

PV

spui

spui PV

PI

explosievat PV

monstername

thermokoppels

buffervat PV

PV

drukopnemer (Baldwin)

thermokoppels

spui

drukopnemer (Kistler)

monstername

Figuur 1: Experimentele testopstelling.

Resultaat Geen reactie Zelfontsteking

Temp.a en rel. drukstijging < 50 K en < 10% > 50 K of > 10%

Ontstekingsuitsteltijd > 15 min < 15 min

Tabel 2: Zelfontstekingscriterium voor propaan en butaan mengsels.

Zelfontstekingsgrenzen propaan/n-butaan/i-butaan De zelfontstekingsgrenzen van propaan, n-butaan en i-butaan in lucht zijn experimenteel bepaald bij begindrukken tot 30 bar en voor een breed concentratiegebied. Uit figuur 2 blijkt dat de zelfontstekingstemperaturen (AIT) significant dalen bij toenemende druk. Voor een concentratie van 40 mol% propaan in lucht is de AIT gelijk aan 573 K bij atmosfeerdruk en daalt tot 523 K bij een druk van 1.5 MPa. Deze AIT’s zijn veel lager in vergelijking met de AIT van propaan (763 K) bepaald volgens de standaard methode EN 14522 (2003). De propaanconcentraties met de laagste zelfontstekingsgrenzen zijn rijke concentraties met een equivalentieverhouding van meer als 10. Deze concentraties zijn bovendien drukafhankelijk. De aanwezigheid van resterende verbrandingsproducten en roestvorming in de explosievaten zorgen voor een grote spreiding tussen de verschillende testreeksen, voornamelijk bij hoge druk, zie figuur 2. De zelfontstekingsgrenzen van n-butaan/lucht mengsels liggen ongeveer 25 K lager in vergelijking met de grenzen van propaan/lucht mengsels, zie figuur 3. Dit kan verklaard worden door de hogere ketenlengte van n-butaan ten

135

3 Experimentele studie

Equivalentieverhouding [-] 0

10

5

40

20

2.5 523 K Eerste reeks 523 K Derde reeks 548 K Eerste reeks 548 K Derde reeks 573 K Eerste reeks

Initiële druk [MPa]

2

1.5

1

0.5

0 0

10

20

30

40

50

60

70

80

Molaire fractie propaan [mol%]

Figuur 2: Overzicht van de zelfontstekingsgrenzen van propaan/lucht mengsels. 2.5

503 K Initiële druk [MPa]

2

511 K 523 K

1.5

548 K 1

0.5

0 0

10

20

30

40

50

60

70

80

Molaire fractie n-butaan [mol%]

Figuur 3: Overzicht van de zelfontstekingsgrenzen van n-butaan/lucht mengsels.

opzichte van propaan waardoor het gemakkelijker is om methylradicalen af te splitsen. De zelfontstekingsgrenzen van i-butaan/lucht mengsels komen goed overeen met de zelfontstekingsgrenzen van propaan/lucht mengsels. Eveneens zijn de zelfontstekingsgrenzen van twee LPG/lucht mengsels bepaald voor verschillende concentraties en begindrukken. Het eerste LPG mengsel bestaat uit 50 mol% propaan en 50 mol% n-butaan en het tweede LPG mengsel bestaat uit 40 mol% propaan, 30 mol% n-butaan en 30 mol% i-butaan. Figuur 4 toont aan dat de minimale zelfontstekingsdrukken van de twee LPG/lucht mengsels goed overeenkomen met de grenzen van de component met de laagste zelfontstekingstemperatuur, namelijk n-butaan. De ligging van de zelfontstekingsgebieden geeft een verklaring voor het verloop van de bovenste explosiegrenzen van propaan waargenomen door Van den Schoor (2007). De bovenste explosiegrens van propaan/lucht mengsels vertoont bij een druk van 1.0 en 1.5 MPa en bij een temperatuur vanaf 523 K een meer dan lineaire toename (Figuur 5). Deze afwijking kan verklaard worden door de nabijheid van het zelfontstekingsgebied.

136


1 AIT LPG (40/30/30)

Initiële druk [MPa]

0.9

AIT LPG (50/50)

0.8

AIT n-butaan 0.7 0.6 0.5 0.4 0.3 0.2 10

20

30

40

50

60

70

80

Molaire brandstof fractie [mol%]

Figuur 4: Vergelijking van de zelfontstekingsgrenzen van 2 LPG/lucht mengsels met de zelfontstekingsgrenzen van n-butaan/lucht mengsels bij een temperatuur van 523 K.

Molaire fractie C3H8 [mol%]

70 UFL 3.0 MPa

60

UFL 2.0 MPa 50


40


30

UFL 0.1 MPa 20

AIT 1.0 MPa AIT 1.5 MPa

10 0 280

330

380

430

480

530

580

630

Temperatuur [K]

Figuur 5: Vergelijking van de bovenste explosiegrenzen (UFL) en de zelfontstekingsgrenzen (AIT) van propaan/lucht mengsels.

Het laatste gedeelte van de experimentele studie bestaat uit het bepalen van de zelfontstekingsgrenzen van methaan/lucht mengsels bij verhoogde drukken. Deze experimentele data dienen voor de validatie van het numeriek model en zullen in de volgende paragraaf voorgesteld worden.

4

Numerieke studie

Een numeriek model van het zelfontstekingsproces moet enerzijds de complexe reactiekinetica omvatten en anderzijds de warmteoverdracht goed beschrijven. Omdat het nog niet mogelijk is om de complexe reactiekinetica met honderden reacties en tientallen stofsoorten te koppelen aan een CFD stromingsmodellering, wordt in eerste instantie een 0-D model aangewend om verschillende reactiemechanismen te vergelijken. Uit figuur 6 blijkt dat het methaan reac-

137

5 Numerieke studie

Zelfontstekingsdruk [MPa]

5 NIST GRI 3.0 BGC ENSIC AIT (deze studie)

4

3

2

1

0 580

600

620

640

660

680

700

720

740

Temperatuur [K]

Figuur 6: Vergelijking van de zelfontstekingsgrenzen bepaald met het 0-D model en verschillende reactiemechanismen voor een 60 mol% methaan in lucht mengsel. 5 0-D model 1-D model 2-D model AIT (deze studie)

Pressure [MPa]

4

3

2

1

0 620

630

640

650

660

670

680

690

700

710

720

Temperature [K]

Figuur 7: Vergelijking van de zelfontstekingsgrenzen bepaald met het 0-D, 1-D en 2-D model en het BGC-mechanisme en de experimentele grenzen voor een 60 mol% methaan in lucht mengsel.

tiemechanisme van de British Gas Corporation (BGC) kwalitatief een goede voorspelling geeft van de temperatuursafhankelijkheid van de experimentele zelfontstekingsdrukken. Het absolute verschil in de zelfontstekingsdrukken kan deels verklaard worden door de vereenvoudigde 0-D voorstelling van de warmteoverdracht. Voor een betere modellering van de warmteoverdracht en het modelleren van de natuurlijke convectie in het explosievat wordt een 1-D en 2-D model ontwikkeld. Deze modellen maken gebruik van het BGC reactiemechanisme (21 stofsoorten en 55 reacties) voor de simulatie van de warmteproductie. De zelfontstekingsgrens bepaald met het 2-D CFD-kinetisch model vertoont een goede overeenkomst met de experimentele data (figuur 7). Tenslotte wordt het 2-D model toegepast om de volumeafhankelijkheid van de zelfontstekingstemperatuur in sferische en cilindrische volumes te onderzoeken.

138

5


Conclusies en aanbevelingen

Deze studie omvat een theoretisch gedeelte waarin een overzicht is gegeven van de verschillende parameters die de zelfontstekingstemperatuur beïnvloeden en waarin een aantal bestaande zelfontstekingstheorieën worden beschreven. De experimentele studie omvat de generatie van een uitgebreide dataset van zelfontstekingstemperaturen bij verhoogde drukken voor verschillende lagere alkaan/lucht mengsels. Deze data kunnen aangewend worden voor het inschatten van het zelfontstekingsrisico in industriële processen en dienen eveneens voor de validatie van numerieke modellen. De numerieke studie bestaat uit de ontwikkeling van een model die een koppeling maakt tussen de reactiekinetica en de stromingsmodellering, zodat een nauwkeurige voorspelling van de zelfontstekingsgrenzen bekomen wordt. Ondanks het feit dat deze studie belangrijke stappen verwezenlijkt heeft op experimenteel en numeriek vlak voor het inschatten van het zelfontstekingsrisico bij verhoogde druk, is er nog steeds plaats voor verder onderzoek. Op experimenteel vlak kunnen experimenten met ethaan/lucht mengsels de reeks van de lagere alkanen vervolledigen. Verder kan de invloed van de oxidator nagegaan worden door experimenten met zuurstofverrijkte lucht uit te voeren of met andere oxidatoren zoals lachgas (N2 O). Eveneens kan de invloed van andere parameters, zoals de volumeafhankelijkheid, het materiaaleffect en de turbulentie of de ontsteking aan hete oppervlakken nog experimenteel onderzocht worden. De numerieke simulaties met propaan/lucht mengsels toonden aan dat er nog veel werk te verrichten op vlak van modellering van de reactiekinetica van de lagere alkanen bij verhoogde drukken. Het ontwikkeld 2-D model van deze studie kent nog vele toepassingsmogelijkheden, bijvoorbeeld voor zelfontsteking in stromende fluïda of voor de ontsteking aan hete oppervlakken. Het numeriek model kan nog uitgebreid worden met oppervlaktereacties aangezien deze eveneens een invloed hebben op de zelfontstekingstemperatuur van gasmengsels.

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Curriculum Vitae Frederik Norman was born in Kortrijk (Belgium) on December 13, 1980. He graduated as Burgerlijk Werktuigkundig-Elektrotechnisch Ingenieur, optie Mechanica, at the Katholieke Universiteit Leuven in 2003. His masters thesis was on the design of a micro compressor and the optimisation of a turbine for the generation of mobile electrical energy. In August 2003 he started his doctoral study on the influence of process conditions on the auto-ignition temperature of gas mixtures, under the supervision of Prof. dr. ir. Jan Berghmans and Prof. dr. ir. F. Verplaetsen, funded by the Institute for the Promotion of Innovation by Science and Technology in Flanders (IWT), scholarship (2004-2007). In 2006, he received the award for the the best student poster on the 13th International Heat Transfer Conference, Sydney, Australia.

List of publications International journals with review Norman, F., Van den Schoor, F. and Verplaetsen, F. (2006), Auto-ignition and upper explosion limit of rich propane-air mixtures at elevated pressures, Journal of Hazardous Materials 137, 666–671. Van den Schoor, F., Norman, F. and Verplaetsen, F. (2006), Influence of the ignition source location on the determination of the explosion pressure at elevated initial pressures, Journal of Loss Prevention in the Process Industries 19, 459–462. Van den Schoor, F., Norman, F., Tangen, L., Sæter, O. and Verplaetsen, F. (2007), Explosion limits of mixtures relevant to the production of 1,2 dichloroethane (ethylene dichloride), Journal of Loss Prevention in the Process Industries 20, 281–285.

Proceedings of international symposia with review Norman, F., Vandebroek, L., Verplaetsen, F. and Berghmans, J. (2006), Numerical Study of the Auto-Ignition in Methane/Air Mixtures, IHTC 13, Sydney, Australia. Norman, F., Vandebroek, L., Verplaetsen, F. and Berghmans, J. (2007), Influence of ammonia on the auto-ignition limits of methane/air mixtures, Proceedings of the 3rd European Combustion Meeting, Chania, Crete, Greece. Norman, F., Verplaetsen, F. and Berghmans, J. (2007), Experimental validation of auto-ignition models for methane/air mixtures at elevated pressures,

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Proceedings of the 5th Int. Seminar on Fire and Explosion Hazards, Edinburgh, United Kingdom.